From what I’ve ‘heard’ at times there are select prophecies in the Old Testament that are apparently a reference to Jesus.
Are there only a select few, if so which are they? Or are they a truly boundless list which does not bare mentioning.
It depends who you ask. Probably somewhere between 30 and 400. Either way, a very compelling, large number that has an insanely low probability and makes both the existence of God and the truth of Christianity quite probable.
Even if you don't want to read my discussion, I encourage you to explore the topic yourself with these resources.
The Prophecy Knowledge Handbook is nice because it includes an Appendix that has 1) the prophecy, 2) a star if it is a Messianic prophecy, 3) Scripture where predicted, 4) where it is fulfilled (in the specific Scripture or in a certain historical event). Walvoord in this book notes 100 Messianic prophecies (includes fulfilled and unfulfilled).
I also know there have been many probabilistic analyses on the prophecies of Jesus. If I or someone else can find some, it would be worth mentioning here. While assigning probabilities to the various prophecies can be difficult (read "arbitrary"), it still gives an appreciation for the divine orchestration at work.
I guess I also have to mention somewhere explicitly that prophecy is significant because it is telling the future far in advance; in this case, it is hundreds of years in advance, and 1,400 years in advance regarding Genesis 3:15. What prophecy isn't: changing the reliable dating of every book of the Bible ever to conform to a naturalistic presupposition that denies miracles or the supernatural. Thanks but no thanks liberal scholars (see vaticinium ex eventu for a brief [liberal] perspective on this topic).
I can give you some information and resources that address your question, but I don't think I can offer a definitive answer; I hope to improve the content of this answer with time. It is a good question without an agreed-upon answer, but that doesn't mean there is not a correct answer or a worthwhile answer that deserves investigation. This answer currently is more of a landscape view than diving into the details. I include references at the beginning and end for further study, and I hope to update this answer to make it better in the future. (Such as actually including specifics in each of the 4 categories).
There are few different categories of "prophecies about Jesus" depending on who came to that conclusion. I think this distinction is worthwhile, especially in the notable differences between groups 1 and 2.
When rejecting Jesus as Messiah, Jews often cite currently unfulfilled Messianic prophecies as the reason. Christians, however, understand that these prophecies were not meant to be fulfilled during Jesus' first coming on Earth, but during His 2nd Coming and the Millennial Reign. Also, note that by modern Jews, I mean followers of modern Rabbinic Judaism.
Even the Jews do not agree on what constitutes a Messianic prophecy. See some of the Scriptural requirements of the Messiah and the mention of the disagreement among Jews.
The New Testament authors understood Old Testament prophecies in ways that modern Jews do not, and modern Christians probably wouldn't have if the NT authors did not "begin the trend"/figure it out. They understood the "dual fulfillment" nature of some prophecies, such as the virgin birth, etc. These prophecies are more explicit and could be more readily counted. It may be also worth further distinguishing the prophecies that Jesus explicitly taught about himself.
Take the virgin birth prophesied in Isaiah 7:14, for example. This had a historical fulfillment in Isaiah 8-9, and yet was also cited as being fulfilled in Jesus in Matthew 1:22-23
Matthew 1:22-23 All this took place to fulfill what the Lord had spoken by the prophet: "Behold the virgin shall conceive and bear a son, and they shall call his name Immanuel" (which means God with us).
A good and important question in understanding the discrepancies between how Jews and Christians understand Messianic prophecy would be, "Do Jews recognize the nature and validity of dual fulfillment prophecy?"...Welp, I don't know. A good question to ask (probably best for Judaism.SE). I would be curious if they recognize any prophecies as having a historical fulfillment and then another fulfillment later on, such as by the Messiah. The discussion in Evidence that Demands a Verdict suggests that they don't explicitly recognize this, but they do recognize multiple levels of meaning in the Tanakh (Old Testament). This understanding of multi-faceted meaning is exemplified in the Midrash commentary.
These come from the further examination of Scripture by later people, mostly Christians, from the church Fathers to today. The "addition" of other Messianic prophecies stems from the understanding that the NT authors were not exhaustive in the application of Old Testament prophecy to Jesus Christ as the fulfillment. For example, the NT authors never said, "Hey guys, Jesus didn't fulfill all the Messianic prophecies but he will fulfill all the not-yet-fulfilled ones in His Second Coming!" I am curious how many prophecies we understand as Messianic today that weren't explicitly mentioned in NT, or how our understanding morphed in the first few centuries of church fathers. Hopefully, I will find the answer and update it.
I'm not absolutely certain of any specific examples of prophecies accepted by Christians that aren't mentioned in the New Testament, though I imagine there are many. For example, my references above lists 351 prophecies fulfilled in Jesus, and I don't think all of these (or even the 45 listed) are all explicitly identified in the NT. I'd rather double check than state an incorrect one.
Typology (see GotQuestions) is a symbol or foreshadowing of things to come, in this case of Jesus the Christ (Messiah). In The Prophecy Knowledge Handbook, "types" or "typologies" are counted as Messianic prophecies. I agree with this analysis, especially because when (all 3 of my examples) are explicitly applied to Jesus in the New Testament. They are a noteworthy, distinguishable subclass of Messianic prophecy.
Examples of typology
Jesus as the Passover Lamb
Jesus as the bronze serpent (Numbers 21:4-9, John 3:14-15)
In Numbers, God sent fiery snakes on the Israelites as a deadly punishment for their sin (speaking against God aka complaining). Then, they repented, and God directed Moses to put a bronze serpent on a pole, and everyone who is bitten who looks to the pole will live through the deadly snake bite. In comparison, all have earned a deadly punishment for their own sin, and all who look to Jesus will be saved from it. Jesus states in John,
John 3:14-15 "Just as Moses lifted up the snake in the wilderness, so the Son of Man must be lifted up, 15 that everyone who believes may have eternal life in him.”
There are a few less obvious allusions to the bronze serpent typology by Jesus discussed here. I just discovered this typology while listening to Evidence Demands a Verdict on the way to work today, and I have to say, that's so cool!
I would like to add a prophecy not in the lists of 45 or 351 prophecies given by @alexstrasser:
He alone stretches out the heavens and treads on the waves of the sea. (Job 9:8)
St. John Chrysostom took this to be a prophecy of Jesus walking on the water.