Bring a large pot of generously salted water (1-2 tablespoons salt) to a rolling boil. Cook pasta according to package instructions until al dente. Before draining, reserve 1/4 cup of pasta cooking water, then drain the pasta.

Heat olive oil and butter in a large 12-inch pan over medium heat until butter foams. Add oyster mushrooms, spreading them out as much as possible, and cook for 5-7 minutes without stirring initially, until golden brown and tender with edges curled.

Add minced garlic and thyme to the mushrooms. Sauté for 30 seconds, stirring constantly, until fragrant. Be careful not to burn the garlic.

Lower heat to medium-low and pour in heavy cream, stirring to incorporate the browned bits from the pan. Stir in grated Parmesan cheese until melted and smooth.

Season sauce with salt and black pepper to taste. Add reserved pasta water 1-2 tablespoons at a time, stirring between additions until you achieve desired sauce consistency.

Add drained pasta to the sauce and toss with tongs for 1-2 minutes until every strand is well coated and everything is heated through.

Serve immediately, garnished with fresh parsley or chives and extra grated Parmesan cheese.