Crack the eggs into a bowl, add salt and milk or water, set aside. Blanch the tomato, remove the skin, cut into quarters, remove the seed cavities along with the juice. Finely chop the flesh, pressing gently by hand, and set aside.
Heat a small pan (about 18 cm diameter) over medium heat, add half a tablespoon of butter and melt. Add the chili pepper, increase the heat and add the tomatoes. Fry over higher heat for a few seconds until the tomatoes release their liquid but remain firm (there should be no juice on the pan). Meanwhile, whisk the eggs (with a whisk, beater or fork) combining the whites and yolks into a uniform mixture.
Add the remaining butter to the pan with tomatoes and spread it across the pan. Pour in the egg mixture (heat should still be quite high). Move the pan to distribute the egg mixture evenly across the entire surface of the pan, then place back on the heat for a few seconds until the bottom sets (see video at the bottom of the page under the photos).
Begin moving the pan vigorously back and forth so the egg mixture slides quickly. Remove the pan from the heat from time to time. The omelet should puff up quickly and begin to set. The omelet should cook very quickly, so it stays fluffy, soft, tender and moist. A good omelet should melt in your mouth, it should never be overcooked and browned on the bottom.
When the omelet is almost completely set but the top remains moist, add the red paprika powder and cheese. Using a spatula, fold the omelet in half (it may tear, but don't worry about it) and transfer to a plate. Sprinkle with freshly ground pepper, mint or basil.
