Take the eggs out of the refrigerator an hour before you cook. If you forget, you can microwave them two at a time for fifteen seconds each. (The authorities forbid this, but I've never had a problem with it.)
Break the eggs into a cup first (to check for bad ones) and then dump them into a bowl. Add 1/4 cup water mixed with the Tabasco, and whisk until well blended.
Using an omelette pan (or a skillet with rounded sides), melt 1/2 Tbs. of the butter over medium-high heat, swirling it around until it bubbles. Before it gets a chance to brown, add one-fourth the egg mixture.
Here's where it gets tricky. As soon as the eggs are in the pan, begin to agitate the pan with rapid jerks so that liquid egg constantly flows beneath the egg that has set. When there is no more liquid flowing, the omelette is finished. This entire process should take less than a minute. Remove from the heat.
Put one-fourth of the tomato, basil, and cheese in a line across the center of the omelette and, using the pan (or, if you must, a rubber spatula) fold the egg over the ingredients and slide it onto a plate. Keep warm while making the remaining omelettes.