Eggs, like any protein-rich food, toughen when subjected to heat, and need to be treated just as carefully as you would, say, a fillet steak. The technique both with fillet steaks and with omelettes is to cook them rapidly; making an omelette, you push the set edges towards the centre of the pan, allowing the runny egg to fill the vacated space and to set as fast as possible.
Cold omelettes -- tortillas, frittatas and so on -- usually contain various extra ingredients, and are difficult to manipulate. So, instead of cooking them at such speed that they do not have a chance to think about toughening, you try the opposite approach: slow cooking.
These omelettes are often quite thick. I admire their makers. I have found that more than five eggs in my 28 cm frying pan take so long to set that they become rubbery.
Crack five eggs into a bowl, beat them gently with a fork until the whites and yolks are just blended (experts tell you that the eggs for an omelette should not be beaten thoroughly -- I have never done comparative tests), and stir in three tbsp of cheese (I used Gruyere). Melt 30 g to 40 g of butter in a 28 cm frying pan on a very low heat. Pour in the eggs, and cook until the surface is starting to set.
Now, you can attempt the classic method of inverting the pan over a plate and sliding the upside-down omelette back into it -- a procedure I have never dared attempt. Or you can do what I do: flash the omelette under the grill for a minute or so. The heat of the grill is high: remove the pan as soon as the runny egg starts to set, because the cooking will continue.