Unable to compile dependency which contains nifs relying on additional libs (homebrew)

I’m a little bit lost, during mix deps.compile a dependency is unable to compile because the include path of homebrew is not included (/opt/homebrew/include) and maybe also the lib directory. I think I was facing the same problem on my previous Mac, but I do not remember how to fix this issue anymore, without modifying the Makefile of the dependency.

find the solution after digging around in Excal issue on M1 macOS - #8 by Jason_P