In a large bowl whisk the eggs with milk, baking powder, salt, and black pepper. Whisk until well combined. Let stand at room temperature for at least 5 minutes.
Heat a large non-stick skillet over medium-high heat. Add butter and melt until sizzling. Whisk eggs again briefly then mix in the cheddar cheese (if using). Pour the egg mixture into the hot skillet. Stir constantly with a spatula until the eggs have reached desired consistency.