Bring 6 quarts of salted water to a boil in an 8-quart pot over high heat.
Heat the olive oil in a large skillet over medium heat.
Scatter the garlic & crushed red pepper flakes over the oil and cook, shaking the pan, until golden, about 2 minutes.
Add as many of the mushrooms as will fit comfortably into the skillet.
Season lightly with salt and pepper and toss in the sage.
Add the remaining mushrooms as the mushrooms in the skillet wilt and make room.
Cook, stirring and tossing frequently, until the mushrooms are sizzling and brown, about 10 minutes. (If the mushrooms have given off a lot of water during cooking, you’ll have to wait for that liquid to boil off before the mushrooms begin to brown.).
Stir the spaghetti into the boiling wate; return to a boil, stirring frequently.
Cook the pasta, semi-covered, stirring occasionally, until done, about 8 minutes.
Add the stock to the browned mushrooms, bring to a boil, and lower the heat so the sauce is at a lively simmer.
Cook until the liquid is reduced by about half, about 5 minutes.
If the skillet is large enough to accommodate the sauce and pasta, fish the pasta out of the boiling water with a large wire skimmer and drop it directly into the sauce in the skillet.
If not, drain the pasta, return it to the pot, and pour in the sauce.
Toss in the parsley and bring the sauce and pasta to a boil, stirring gently to coat the pasta with sauce.
Check the seasoning, adding salt and peppers if necessary.
Remove the pot from the heat, stir in the cheese, and serve immediately in warm bowls.