When you’re making an omelette, you want two conditions: enough cooking fat and a thoroughly heated skillet.
This is about 1 tablespoon butter. If you don’t have enough cooking fat, your eggs will stick to the bottom of the pan. If they stick, the omelette can break apart and lose its shape.
Ideally the pan should be hot enough but not so hot that the butter begins to brown. If your pan isn’t sufficiently heated, the eggs won’t set and it’ll take longer than usual to cook. On the other hand, if you wait too long, the butter will burn. As you can see in the bottom pic, I waited 30 seconds too long before adding the eggs. A perfect omelette should be light and golden throughout without any visible browning.
Allow the butter to sizzle and the foam to subside, then add 2 to 3 beaten eggs and let them sit for about 30 seconds to a minute. With a fork or spatula (assuming you’re using a nonstick pan), draw the lightly cooked egg toward the center of the pan. As you do so, tilt the pan so that any uncooked beaten eggs flow into the bare part of the pan. Repeat this process as you work your way around the pan. After a few seconds, there should be just a little moist egg remaining. Add your filling, if any, then tilt the pan away from you. Tap the handle lightly; the far edge should fall back on itself, then turn the pan over a plate so that the folded omelette falls out.
For the pan-glazed tomatoes: Take a handful of small grape or pear-shaped heirloom tomatoes and toss them onto a hot pan along with some melted unsalted butter or other cooking fat. Cook until the tomatoes wilt slightly and/or begin to burst, about 30 seconds. Remove pan from heat; garnish omelette and serve immediately.
Omelette with peperonata filling, pan-glazed heirloom tomatoes