It's really hard to get a perfect omelet in a restaurant, let alone at home. If you want to make sure the cheese melts the eggs will have gotten tough, rubbery, or dry. If you want the eggs tender and moist, the cheese won't have a chance to melt. And personally, most of the omelets I'm served - I feel the eggs are too thick - they should be thin, tender and yet somehow, somehow, the lavish amount of cheese I want should somehow be able to be nice and melted.
Impossible? Only a dream? Well, I did a lot of research and development and today I achieved the impossible dream.
The trick is you pour in the eggs and you do not touch them. Just pour them in, and cover them on a very low flame.
This is for a 4 egg cheese omelet - basically 2 servings. You need a 12" non-stick pan that still has its non-stick abilities intact and a cover that is sort of flat rather than a high dome (to concentrate the low heat). With a fork, whip up the eggs with about 1 1/2 tablespoons of water. Crumble 8 oz. cheese of your choice. If you freeze the cheese first and then defrost, even semi soft cheeses crumble instantaneously. Melt about 1 T butter to cover bottom of pan. Heat pan on a VERY low flame and pour in the eggs. Cover and do not open for 5 minutes. When eggs appear cooked (surface is not liquidy looking) spread on the cheese and maybe some very thin sliced scallions, cover, and turn off the heat. Drop the toast and by the time it's buttered you can fold the omelet in half to enfold the melted cheese inside the egg, and serve. The egg layers are only 1/4" thick. It's beautiful, delicate, tender - perfect.
Really good with some home made cooked salsa spread on top.