Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.
In a large skillet, heat the butter and olive oil over medium heat until melted and hot.
Add the sliced mushrooms to the skillet and sauté for 6-8 minutes, stirring occasionally, until the mushrooms are browned and have released their moisture.
Add the minced garlic, salt, black pepper, dried thyme, and dried oregano to the mushrooms and cook for 1-2 minutes until fragrant.
Pour in the white wine and cook for 2-3 minutes, stirring occasionally, until the wine has mostly evaporated.
Reduce the heat to low and stir in the heavy cream. Simmer gently for 3-4 minutes until the sauce thickens slightly.
Add the grated Parmesan cheese to the sauce and stir until melted and combined.
Add the cooked fettuccine pasta to the skillet and toss well to coat the pasta evenly with the creamy mushroom sauce.
Remove from heat and sprinkle the chopped fresh parsley over the pasta.
Serve immediately while hot.