Heat oven to 400°F. Arrange bacon on a rimmed baking sheet and cook 15-20 minutes until crisp; drain and crumble.

Make four omelets separately. For each, whisk 3 eggs, 1 tablespoon milk, one quarter of the salt and pepper.

Melt 1 tablespoon butter in an 8-inch nonstick skillet over medium-low heat. Pour in the eggs. After 30 seconds, push set edges inward and tilt to distribute uncooked egg.

When nearly set, put one quarter of the bacon and 1/4 cup cheddar over half the omelet. Fold and continue cooking gently until no liquid egg remains and the center reaches 160°F, about 4-6 minutes total.

Serve immediately and repeat with remaining ingredients.