I like crispy omelettes too, so here's how I make them:-
1/2 finely chopped onion
1 clove garlic, finely chopped
1/2 chopped red pepper
1 large flat mushroom, thinly sliced
1/4 chopped fresh chilli
2 eggs (free range), beaten to within an inch of their lives, then passed through a really fine mesh sieve
3 oz grated strong cheddar (smoked Applewood is really good)
Fry the onion, garlic, pepper, chilli and mushrooms in a little olive oil or butter until virtually cooked (using a heavy duty frying pan if possible). Remove the vegetables and place them on a piece of kitchen towel to absorb any excess oil. Pour the beaten and sieved egg into the same frying pan and allow to cook over a gentle heat until the egg starts to set. Gentle arrange the vegetables back over the omelette, add the grated cheese and place under a hot grill to brown and puff up.
I don't like raw (ie runny) egg, nor do I like to eat the stringy bits from the white of an egg, which is why I sieve it (it also catches any bits of egg shell). I don't know anyone else who sieves egg, so maybe I'm just a bit bonkers !