Years ago, at a roadside coffee shop (Waddle’s at Jantzen Beach in Portland, OR), I had what I'd call the Platonic ideal of cheese omelets. It was totally unexpected, and it was a revelation: thin and light, creamy and at the same time fluffy, cooked just so, with the cheese melty but not overdone or running out the sides. I've never had one quite like it, and I've never even come close when I've made them at home.
My home-made omelets always come out dry and spongy. I suspect I'm over-cooking them but I'm not even sure about that. I've tried adding no liquid, adding a little milk, adding cream, adding half-and-half...haven't hit on the right formula. I usually cook them in butter, in a non-stick pan, over medium-high heat. I generally rip them to shreds when I try to turn them, but I could live with that if I could just get the texture right--I wouldn't care if they were pretty and neat, if they just had that perfect texture.