> how it can turn recursive structures like expressions and statement blocks into linear sequences of instructions

I think this is one of the key concepts in a compiler, yet I don't think it has much to do with parsing.

Parsing (in a compiler) is the act of taking a linear sequence of characters or tokens, and turning them into a rich AST structure.

The back end of the compiler is what takes this recursive structure and flattens it out into a linear sequence of instructions that "mean" the same thing as the tree.

Parsing is critical, of course, for building a working compiler. But I think not focusing on surface syntax gets to the key recursive-to-linear insight you mention more directly!