In a large pot, bring salted water to a boil. Add the cheese tortellini and cook according to the package instructions until al dente. Drain and set aside.
In a large skillet over medium heat, add the olive oil. Once hot, add the sliced mushrooms and sauté for about 5-7 minutes, or until golden brown and tender.
Add the minced garlic to the mushrooms and sauté for an additional 1-2 minutes, until fragrant, being careful not to burn the garlic.
Pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan cheese, dried thyme, salt, and pepper. Allow the sauce to thicken slightly, about 3-4 minutes.
Add the cooked tortellini to the creamy mushroom sauce, gently stirring to coat all the pasta evenly in the sauce.
Taste the dish and adjust the seasoning with more salt and pepper if necessary. Remove from heat.
Serve immediately, garnishing with chopped fresh parsley for color.
Notes
Feel free to use any variety of mushrooms you prefer.