Profiling the C++ compilation process
Clang 9 (and newer) has a -ftime-trace flag, which makes it output a profiling report as JSON (in addition to an object file).
You can import this file into a profiler that comes with Chrome (chrome://tracing) to get a nice visualisation:
The bars correspond to headers that had to be parsed, and for each header, specific classes (and probably other constructs) that had to be parsed. It also reports time spent on instantiating specific templates.
There's a tool from the Boost project, which could be useful for pretty much any compiler and build system.
The tool requires source code instrumentation with TEMPLATE_PROFILE_ENTER() and TEMPLATE_PROFILE_EXIT() macro calls. These macros then generate specific diagnostics (warnings) at compile-time, which are timed and collected along with instantiation callstacks (which consequently allow building and visualizing callgraphs) by a script. Not bad, IMO.
I didn't use it yet though.
For GCC there are debugging options to find how much time is spent within each of the phases of C++ compilation?
-Q Makes the compiler print out each function name as it is compiled, and print some statistics about each pass when it finishes.
-ftime-report Makes the compiler print some statistics about the time consumed by each pass when it finishes.
Passes are described in GCCINT 9: Passes and Files of the Compiler.
You can post output of g++ compilation of single source file with -v -ftime-report here to discuss it. There could be some help on the GCC mailing list.
For compilers other than GCC (or GCC more ancient than 3.3.6) see the other options in this thread.