Prepare the filling. Make sure the bacon and sausage are fully cooked and crumbled, and the ham is cooked and chopped. Shred the cheddar cheese if needed.
Whisk the eggs. Crack the eggs into a small mixing bowl. Add the freshly ground black pepper and whisk until the yolks and whites are evenly combined.
Heat the skillet. Place a 10-inch nonstick skillet over medium heat. Add the butter and swirl the pan until the bottom is evenly coated.
Add the eggs. Pour the beaten egg mixture into the skillet, tilting the pan slightly to spread it into an even layer.
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. Cook for approximately 3–4 minutes, or until the egg mixture is mostly set and the omelet can be folded without breaking.
Add the cheese and meats. Sprinkle the shredded cheddar, crumbled bacon, cooked sausage, and chopped ham evenly over one half of the omelet.
Fold the omelet. Carefully lift the unfilled half with a spatula and fold it over the filling.
Melt the cheese. Cook for approximately 1 additional minute, or until the cheese is melted and the eggs are fully cooked. The center should reach 160°F (71°C).
Serve immediately. Carefully slide the omelet onto a serving plate and enjoy while hot.