• 1 1/2 lb. mixed mushrooms (such as crimini, shiitake, oyster, and/or maitake), torn into 1" pieces
• 4 sprigs thyme, plus leaves for serving
• 6 garlic cloves, smashed
• Kosher salt, freshly ground pepper
• 1/4 cup extra-virgin olive oil
• 2 Tbsp. unsalted butter
• 4 oz. Parmesan, finely grated, plus more for serving
• 1 Tbsp. red wine vinegar