Place egg whites in a large bowl, and the yolks in a separate small bowl. Whisk the yolks, salt, and pepper together, and set aside.
Using an electric or stand up mixer, beat the egg whites until soft peaks have formed (how to tell: stop the mixer and lift from the eggs--The eggs should form peaks that hold their shape but are not overly stiff/dry.).
Spoon 1/3 of the whisked egg whites into the yolks, and stir together, trying to keep as light and fluffy as possible, but know it's hard to do at this step. Add the remaining egg whites, and fold them into the yolks with a rubber spatula, trying as hard as possible to not deflate the egg whites. Fold until no streaks remain.
Melt butter in a 9" pan over medium heat. Once the butter is foaming, add the eggs and gently spread into the pan using your spatula. Sprinkle cheese on half the omelette, then cover your pan with a lid. Continue to cook until the cheese has melted, and the eggs on top have set, about 4 more minutes.
Use a spatula, or 2 if necessary, to fold the omelette over itself. Continue to cook in the pan, uncovered, for 1 more minute. Slide onto a plate, top with chives and tomatoes, and enjoy!