Cook the fettuccine or spaghetti according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil and butter over medium heat. Add the chopped onion and sauté for about 3-4 minutes until softened.
Stir in the minced garlic and sliced mushrooms. Cook for an additional 5-7 minutes, or until the mushrooms are browned and have released their moisture.
Add the dried thyme, salt, and black pepper to the skillet, stirring to combine.
Pour in the heavy cream and bring to a gentle simmer. Cook for 2-3 minutes, allowing the sauce to thicken slightly.
Stir in the grated Parmesan cheese until melted and well combined. If the sauce is too thick, add a little reserved pasta water to reach desired consistency.
Toss the cooked pasta with the creamy mushroom sauce until evenly coated.
Serve immediately, garnished with fresh parsley and additional Parmesan if desired.