There are languages like Verilog/VHDL that help out with most of it. You write the design in a language like any other programming language and a program will compile it down to a design
Edit 1: For context, an entire assignment of one class I had back in college was to code up an entire processor using Verilog that ran custom instructions. The professor then would run your processor with a set of instructions (unique for each student) and you had to get the right result to get a good grade.
Edit 2: yes, there are other ways ICs and processors are made. This is one.
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