Melt a part of the butter and braise the onions and peppers on low heat for about 5 min. Leave them aside.
Beat the eggs in a bowl. Smear a pan with the remaining butter and pour the eggs in it. Sprinkle with salt and black pepper.
Fry the omelette, turn it over carefully and fry on the other side.
Pour the filling with the peppers in the middle of the omelette, sprinkle with grated cheddar, roll it up and serve while still warm.