In a medium bowl, beat the eggs, water, and salt until well combined.
In a saucepan over medium-low heat, melt the butter and add chopped onions and bell peppers.
Stir until the onions and peppers are soft but not browned.
Add diced ham, bacon, and sausage to the vegetables. Cook until the meats are heated through.
Pour the egg mixture into a preheated non-stick skillet or griddle.
Cook until the eggs are nearly set but still glossy on top.
Add the meat and vegetable mixture evenly over one side of the omelette.
Sprinkle the cheese on top of the filling and carefully fold the other side over to create a half moon.
Cook until the cheese is melted and the eggs are fully set.