In a very large bowl, whisk together eggs, milk, salt and pepper. In a large skillet, melt butter over medium heat; pour in egg mixture. Cook over medium heat, without stirring, until mixture begins to set on the bottom and around the edges. With a spatula or a large spoon, lift and fold the partially cooked egg mixture so that the uncooked portion flows underneath. Continue cooking over medium heat for 2 to 3 minutes or until egg mixture is cooked through, but is still glossy and moist. Immediately remove from heat.