Profiling .mexa64 function with `profile`

I have a medium sized code base that at the bottom has a .mexa64 connector to some C functions. As I am making optimizations to that code I want to use the Matlab profile functionality to identify bottlenecks. However profile just tells me how many times the first C function has been called and nothing else.

What I want needs to:

a) Give me a breakdown of time spent in each function (C functions included).

b) Work inside Matlab.

PS1: Yes, I know about codegen, but the functions I use in Matlab cannot be converted.

PS2: Yes, I also know I can write a C file using the MATLAB API to load the data and pass them down, but no, I don't want to write a whole new module to do the same thing as my Matlab code.