Place the butter in a frying pan over a high heat. When the butter is foaming add the mushroom and cook for 2-3 minutes on each side, basting with the butter. Season with salt and freshly ground black pepper.
In separate frying pan, heat the vegetable oil. Crack in the egg and fry the for 1-2 minutes, or until cooked to your liking.
To serve, place the mushroom on a plate, topped by the fried egg.