Prepare the filling. Make sure the bacon and sausage are fully cooked and crumbled, and the ham is cooked and chopped. Have the shredded cheddar ready.
Beat the eggs. In a small bowl, combine the eggs and freshly ground black pepper. Whisk until the yolks and whites are thoroughly blended.
Heat the skillet. Place a 10-inch nonstick skillet over medium heat. Add the butter and rotate the skillet to coat the bottom evenly.
Add the eggs. Pour the beaten eggs into the skillet, spreading them evenly across the surface.
Cook the omelet. As the edges begin to set, gently lift them with a spatula and tilt the skillet so the uncooked egg flows underneath. Continue cooking for approximately 3–4 minutes, or until the eggs are nearly set.
Add the filling. Sprinkle the shredded cheddar cheese, crumbled bacon, cooked sausage, and chopped ham evenly over one half of the omelet.
Fold carefully. Using a wide spatula, fold the unfilled half of the omelet over the meat and cheese.
Finish cooking. Cook for approximately 1 additional minute, or until the cheddar melts and the eggs are fully cooked. For food safety, the center should reach 160°F (71°C).
Serve immediately. Carefully transfer the omelet to a serving plate and enjoy while warm.