Heat the oil and butter in a large sauté pan over medium heat. Once the butter is starting to sizzle, add the mushrooms in a single layer. Let them cook for a few minutes undisturbed. Check the bottom of the mushrooms, and, when they’re golden brown and caramelized on the edges, flip. Continue to cook until the other side is caramelized as well. Add the onions and sauté until softened, about 2 minutes. Stir in the garlic.