An omelette is what you're describing. Omelettes are a versatile and popular US and international breakfast dish. A general summary of omelette preparation:
Filling Ingredients: Cheese, diced veggies (bell peppers, onions, tomatoes, mushrooms), ham, bacon, or other meats are prepared and placed aside.
Eggs: Whisked eggs are added to the hot skillet. A spatula delicately lifts the edges as the eggs set, letting the raw eggs flow underneath.
When the eggs are mostly set but still little liquid on top, evenly spread the fillings over half the omelette.
Folding: The other half of the omelette is delicately folded over the fillings to form a "half-moon" shape.
Cooking Through: The omelette is cooked longer to melt the cheese and finish cooking.
Plating: Carefully slide the omelette onto a platter and top with fresh herbs or salsa.
Omelettes are popular because you can add your favorite toppings and flavors. They are usually served for breakfast or brunch but can be eaten anytime.
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