In the 18th century there began a scholarly endeavor that, though it has greatly morphed over the decades, still persists today. This endeavor, termed The Quest for the Historical Jesus by Albert Schweitzer, is the attempt to get past the wall of the Bible to discern who the real Jesus was that walked and talked 2,000 years ago. Of course, the opinion varies amongst the scholars as to how much one could even know about Jesus. Some (such as Rudolph Bultmann) believed the New Testament is this impenetrable wall that you can't get past to learn about the historical Jesus. Nevertheless, it didn't stop these scholars (termed critical scholars) from formulating conclusions about who Jesus really was.
Of course, many of the them took issue with Paul's portrayal of Jesus. Perhaps the chief of this objection was F.C. Baur who saw that Paul's Jesus was incredibly distinct from the (Petrine) Jesus of the Gospels. The Pauline Jesus is all about the death, resurrection, and penal substitutionary atonement with little to no mention of his earthly ministry prior to his death. The Jesus of the Gospels, however, though they certainly do mention the death and resurrection mostly consist of what Jesus said and did before that point. There are many more precise ways this argument could be described but this will suffice for my purposes.
So the question is, how can we know that the Jesus of Paul is accurate to the Jesus portrayed in the gospels? J. Gresham Machen's The Origin of Paul's Religion has a fantastic chapter entitled Paul and Jesus that I would recommend to anyone wanting to go deeper in this subject. He gives a multifaceted perspective to this. One of the ways he mentioned, however, I find most captivating. That is, though the gospels afford more pages than Paul as to the life of Jesus prior to the passion narrative (1 Cor 11:23-26 is one of the few in Paul's letters), they are in fact both keenly focused on one thing (from which much springs); Jesus' death.
It is obviously true to readers of Paul that he has a very high view of Jesus and is very occupied with atonement theology resulting from Jesus' death (Rom 3:21-31). However, even though the Gospels spend more time on Jesus ministry prior to his death (though they don't mention much about Jesus' boyhood years), it would be dishonest to say they are not chiefly concerned with it. (Now, I'm going to lay my cards on the table and tell you that I am going to assume that the Gospels are "breathed-out" by the same God and that Paul's letters are as well. I could give argumentation for that but I'll save that for another post. I will continue with this assumption.) In fact, we see Jesus talking about his death very early in the Gospels if you were to compare it with Greco-Roman biographies of that period which would often leave the mention of death until the final sentence. On the contrary, the Gospels are hyper-focused on Jesus' death and start discussing it very early (Matt 16:21, Mark 8:31-33, Luke 9:43, John 11:45 though you could certainly argue John 1:29). Thus, as Michael Kruger says, the Gospels are lopsided biographies. Now, where it Is easy to see the structure differences between the Gospels and Greco-Roman biographies, there is a similarity between the Gospels and biographies that speak to their message.
Suppose you were to read a recently-written biography on O.J. Simpson. It would likely mention his growing up in San Francisco, his time as a Heisman-winning football player at USC, and his impressive NFL career that began as being the first pick of the first round in the draft. These are all things that you would expect to find in any biography of Simpson. But suppose this biography were to end with this, you likely would notice a striking omission, namely, the infamous court case over the murder of Simpson's ex-wife Nicole Brown Simpson and Ronald Goldman. In fact, I would imagine that there are many people who know Simpson chiefly if not only by this fact. Any biography worth reading on Simpson would necessarily cover this. That is because when we read biographies we expect them to focus on the main things; what this person is all about. Of course, to say that this court case is what Simpson was "all about" may seem crude but it is, in reality, THE thing that he is known for. Anyone without prior knowledge of Simpson who reads a properly-written biography on him would leave knowing that to undoubtedly be the case
This expectation that we have with biographies is not entirely dissimilar to what takes place with the Gospels. Now, let me be clear that I am not saying the Gospels are merely biographies. They are certainly more than that but they are not less than that. And when we read the Gospels we are confronted in their very structure that Jesus' main thing is his death, resurrection, and the glorious reality that spurns from that. Paul's Jesus is the risen Lord and the Jesus of the Gospels is not at all dissimilar.