Preheat the griddle on medium heat. Crack the eggs into a mixing bowl and whisk until combined. Add salt, pepper and milk to egg mixture, whisk to combine. Set aside.
Turn the griddle down to medium-low heat and let cool off a little. Place 1 Tablespoon butter on the griddle and let it melt, spreading to cover the griddle.
Top middle of eggs with ¼ cup shredded cheese and half of the chopped bacon, fold over both ends with a spatula like a burrito. Move to the cool side of the griddle.