Hello, I have the same problem, today.

In typeshed, cannot use mypy_extensions.VarArg(policy, maybe...), so cannot define the StartResponse type, that the type the function has default arguments.
Basically, using union type, conditional branching is needed.

Why don't you use Protocol, like this?

class StartResponse(Protocol):
    def __call__(
        self,
        status: str,
        headers: List[Tuple[str, str]],
        exc_info: Optional[Any] = None,
    ) -> Callable[[bytes], None]:
        ...

or

class StartResponse(Protocol):
    def __call__(
        self,
        status: str,
        headers: List[Tuple[str, str]],
        **extra: Any,
    ) -> Callable[[bytes], None]:
        ...

That's a good idea! I haven't tried it though.

That's an interesting idea, indeed. Unfortunately, passing in a function where a protocol is expected does not work with mypy 0.620:

from typing import Protocol

class Caller(Protocol):
    def __call__(self) -> None: ...

def call() -> None:
    pass

def func(caller: Caller) -> None:
    pass

func(call)

Although maybe it should? After all, call is a callable object. And it would mean that we could construct any call syntax for functions and don't need special support in Callable for default functions, keyword arguments etc.