Heat a large skillet over medium-high heat. Once hot, add the butter and olive oil. Wait until the butter has melted and the olive oil is hot, then add the sliced mushrooms.
Let the mushrooms brown without moving them, for about 2 minutes. Give them a stir and let them brown for 2 more minutes. Repeat this process until all the mushrooms are golden brown.
Add the minced garlic and cook for one more minute, stirring constantly.
Pour in the white wine and deglaze the pan, scraping to remove any bits and pieces that might have stuck to the bottom. Simmer for one minute.
Add the chicken stock, heavy cream, grated Parmesan, salt, and pepper. Stir until combined and simmer the sauce until the cheese has melted and the sauce is slightly thick, about 2-3 minutes.
Throw in the fresh thyme, adjust the seasoning with salt and pepper if needed, and remove from heat. Serve while hot.