Heat a large dry pan, over medium-high heat. Add the mushrooms and cook undisturbed for 3 minutes, stir and add olive oil and butter. Continue cooking until the mushrooms are caramelized, 3 to 4 minutes. Add the garlic, fresh thyme, salt and black pepper, and sauté for 30 seconds, or until the garlic is fragrant (making sure it does not burn). Add the wine, lower the heat to medium-low, and simmer for 3 to 4 minutes. Add the stock and continue to cooking, 3 to 4 minutes. Slowly stir in the cream, add ¼ cup parmesan cheese and continue to cook until sauce has slightly thickened, about 4 to 5 minutes.