I just finished How to Read the Bible by Marc Zvi Brettler. It was not as historically oriented as Who Wrote the Bible but it was a very good read just the same, steeped in the historical-critical method at a level I could appreciate and understand.
Aside from the obvious caution against reading the (Old Testament) Bible as literal Word of God (something that Catholics should not need to be lectured on), perhaps the most interesting thesis of the book was his argument that the Bible should be read as a “source book” and not a “text book”. By this analogy he means that the (OT) Bible is a collection of writings representing a variety of viewpoints evolving over time. I had suspected something like this but he lays it out fairly convincingly even if the historical-critical method is never as certain as we would prefer.
One of the questions that I have long pondered was why the seeming incongruity between the OT and the NT. This is one possible answer. The OT itself is far more internally incongruent than most non-scholars appreciate. If that is so then we should not be at all surprised to find incongruities between the OT and the NT. We should not be surprised to find Jesus correcting the priests and pharisees.
My impression is that, traditionally, the Catholic Church has avoided this approach and has, instead, maintained the view that Jesus fulfilled the OT or distinguishing between law and tradition (which is sometimes read as written vs. oral Torah) and that this explained the new direction that Christianity took, particularly in ending most of the requirements of the Torah law. Jews, of course, rejected this and insisted on keeping the Torah.
The rabinical tradition seeks to make sense of the OT as a coherent, unified theology. As a textbook. Some Protestantism does the same while other Protestantism almost ditches the OT. Catholicism has always seemed to me to have had an ambivalent and nuanced approach to the OT.