Heat 1 tablespoon olive oil and 1 tablespoon butter in a medium-sized Dutch oven or heavy saucepan over high heat. Sear the mushrooms and pearl onions until they begin to take on a little color— your mushrooms will make a delightful “squeak- squeak” as they’re pushed around the hot pan— but the mushrooms do not yet release any liquid, about 3 or 4 minutes. Remove mushrooms and onions from the pan and set aside.