Whisk eggs, water, salt, and pepper together in a bowl until yolks and whites are completely combined and eggs are light and frothy, about 30 seconds.

Melt butter in an 8-inch nonstick skillet over medium heat. Pour eggs into skillet and stir rapidly for 20 to 30 seconds until eggs are just starting to set. Spread top of eggs in an even layer and let cook until just slightly underdone and shiny. If necessary, move extra raw egg around to the edges of the skillet. Lower heat to medium-low to prevent browning, if necessary.