Bring a large pot of generously salted water to a boil and cook the fettuccine according to package directions until al dente. Reserve ½ cup of pasta water before draining.
While the pasta cooks, heat olive oil and butter in a large skillet over medium-high heat until the butter is melted and slightly foaming.
Add mushrooms to the hot pan and let them cook undisturbed for 2-3 minutes until they begin to brown. Stir and continue cooking for another 3-4 minutes until golden and their moisture has evaporated.
Lower the heat to medium and add the minced garlic, cooking for just 30 seconds until fragrant, being careful not to let it burn.
Pour in the heavy cream and bring to a gentle simmer, then reduce heat to medium-low and cook for 2-3 minutes until it starts to thicken slightly.
Gradually whisk in the Parmesan cheese until fully melted and the sauce is smooth. If the sauce seems too thick, add a splash of the reserved pasta water.
Season with nutmeg, salt, and pepper to taste, remembering that Parmesan already adds saltiness to the dish.
Add the drained pasta directly to the sauce and toss thoroughly to coat every strand. If needed, add more reserved pasta water a tablespoon at a time to reach your desired consistency.
Serve immediately in warmed bowls, topped with additional Parmesan, fresh parsley, and red pepper flakes if desired.