Using Moq to Mock a Func constructor parameter and Verify it was called twice

I don’t think it is necessary to use a mock for the Func.

You can simply create an ordinary Func yourself that returns a mock of IFooBarProxy:

int numberOfCalls = 0;
Func<IFooBarProxy> func = () => { ++numberOfCalls;
                                  return new Mock<IFooBarProxy>(); };

var sut = new FooBar(func);

sut.Process();

Assert.Equal(2, numberOfCalls);