Boil water for pasta and cook according to instructions. Reserve 1 cup of pasta water for future use.
Heat oil and butter in a large skillet over high heat. Add garlic and cook for 1 minute. Add mushrooms and sauté for about 10 minutes. Stir in thyme, Italian seasoning, salt, and pepper.
Stir in the wine and let it cook for 2-3 minutes, until it is mostly evaporated.
Add broth, milk, ¼ cup parmigiano reggiano, brie cheese, salt, and pepper. Simmer for a few minutes, stirring regularly.
Combine the cooked and drained pasta with the mushroom sauce. Add in ¼ cup reserved pasta water until the sauce has a smooth and silky consistency. Continue adding, as needed.
Top with remaining parmigiano reggiano and parsley. Serve immediately.
