I thought that this was the only way to make an omelet until I had the French and American kinds. It's funny; we like ours thin and lightly browned, whereas the classic American version is fluffy and pale yellow. This almost reminds me of a Spanish frittata; you can eat a quarter of it with a small salad and it makes a satisfying light lunch. My mum usually makes this for lunch when she's got a heavy dinner planned. It's one of my dad's favorites! This is also apparently one of those things that you can get at the train stations in India: jump onto the platform, grab a hot "railway omelet" and speed walk to work where you can nosh away in peace. Bliss!
Grab a bowl. Crack the eggs into the bowl and beat until lathery, about 1 minute. Whisk in the onion, chile, cilantro, turmeric, and paprika until well combined. Sprinkle with a big pinch of salt and a few grinds of black pepper.
Grab a 12-inch nonstick skillet. Add the oil and warm over medium-high heat until mildly shimmering but not smoking. Have a spatula/spoonula at the ready. Pour egg mixture into the pan. Grab the spatula/spoonula and, in small circular motions, distribute the onions, chile, and cilantro evenly around the pan. This also helps move some of the uncooked egg down to the surface of the hot pan. Cover and cook for 2 1/2 minutes.
Grab a plate that's as big as your pan. Pull off the lid and look at your omelet. It might still look a little runny, but it shouldn't be super runny. If it is, then cover and cook 1 more minute. Slide the omelet, cooked side down, onto your plate. Then, holding the plate from underneath, put your pan over your plate, and flip so that the uncooked side lands on the pan. Cook, uncovered, another minute.
Slide onto serving plate, cut into 4, and serve.