Crack eggs into a bowl. Whisk or beat together 1 tablespoon of water per egg with a pinch of salt and pepper.
Melt butter in a nonstick skillet over medium-high heat until hot and foamy. Tilt pan to ensure entire bottom is coated with butter.
Add egg mixture to skillet (mixture should set immediately at the edges). As eggs start to set, push the cooked edges toward the center, letting the uncooked portion flow underneath. Repeat until eggs are set and there's no visible liquid.
Spoon your filling on top of one side; fold the other side over filling and cook to desired doneness. Slide the omelet onto a plate.
Omelets cook quickly, so it's a good idea to precook raw filling ingredients before you start your eggs. Plan on 1/3 to 1/2 cup filling per 2-egg omelet.
An 8- or 10-inch nonstick slope-sided skillet with a slippery-smooth surface and slightly thick base that distributes heat evenly is what we reach for when making omelets in the test kitchen. We're not omelet-biased here: They also make short work of grilled cheese sandwiches and quesadillas.
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