Preheat the broiler. In a 10-inch omelet pan, preferably nonstick, melt the butter until the foam subsides. In a medium bowl, combine the eggs and milk and season with salt and pepper. Add the eggs to the pan and cook over high heat without stirring until the edges set. Lower the heat to moderate and lift the sides of the omelet, tilting the skillet to let the uncooked eggs spread underneath. Cook until the bottom is golden and the top is still slightly runny, about 3 minutes.