They say that in order to understand recursion, you must first understand recursion. Once you master that concept, you might decide that it’s time to write your own compiler that can compile itself as a fun side project. According to [Warren] aka [DoctorWkt], who documented every step of writing this C compiler from scratch, a true compiler will be able to do that.
Some of the goals for the project included self-compiling, focusing on a real hardware platform, practicality, and simplicity. [Warren] outlines a lot of the theory of compilers as well, including all the lexical, grammar, and semantic analysis and then the final translation into assembly language, but really focuses on making this compiler one for practical use rather than just a theoretical implementation. He focuses on Intel x86-64 and 32-bit ARM platforms too, which are widely available.
This project is a long read and very thoroughly documented at around 100,000 words, so if you’ve ever been interested in compilers this is a great place to start. There are a lot of other great compiler tools floating around too, like the Compiler Explorer which shows you generated code as you write in a higher level language.