Prepare the Egg Mixture: Crack the eggs into a mixing bowl. Add milk, a pinch of salt, and a pinch of black pepper. Whisk until well combined and slightly frothy.
Cook the Vegetables and Ham: In a medium skillet, melt butter over medium heat. Add diced ham, green bell pepper, and onion. Cook, stirring occasionally, until vegetables are softened, about 5 minutes.
Add Egg Mixture: Pour the egg mixture over the cooked vegetables and ham in the skillet. Let it cook undisturbed until the edges begin to set, about 1-2 minutes.
Add Cheese and Tomato: Sprinkle shredded cheddar cheese evenly over the omelette. Add diced tomato on top.
Finish Cooking the Omelette: Using a spatula, gently lift one edge of the omelette and fold it over the filling. Continue cooking until the cheese melts and the eggs are fully set, about 2-3 minutes.
Serve: Slide the omelette onto a serving plate. Garnish with chopped parsley if desired. Serve hot and enjoy!