In a large pasta pot, bring 4-6 quarts of water to a boil. Add a teaspoon of salt.
Once the water has come to a rolling boil, add the pasta and cook for approximately 10 minutes, until the pasta is al dente. Reserve 1/2 cup of the pasta cooking water, then drain the rest.
For the sauce:
In a medium saucepan, melt the butter with the olive oil and add the garlic. Mix until the garlic is lightly browned and fragrant.
Add in the mushrooms and cook for 5-8 minutes, or until tender and slightly browned.
Remove from the stove, and allow to cool for 3-5 minutes. Add the whipping cream and mix until combined. Make sure that the whipping cream is at room temperature and not cold or it may separate.
Once cream is fully combined, place the pan back on the stove on low heat and add both of the grated cheeses. Mix until cheese is completely melted and evenly combined. Add in 1/4 cup of the reserved pasta water. Mix in the salt and pepper, taste and add more if needed.
Mix the pasta with the sauce and serve immediately. If you prefer a thinner sauce, you can add more pasta water little by little until you get the consistency you like. If you like it as it is, discard the remaining water.
Garnish with fresh thyme and serve.
Notes
Dairy Free Substitutions:
Butter. Swap out regular butter for vegan butter or vegan margarine.
Heavy whipping cream. Instead of using heavy cream, swap it out with unsweetened full fat coconut milk.
Cheese. Substitute the dairy cheese with vegan cheese or dairy-free cheese option.