Beat eggs and water in a large bowl with a fork until combined. Season.
Heat a quarter of the butter in a small frying pan over medium heat. When the butter is foaming, add a quarter of the egg mixture.
Using a wide spatula, gently push the set egg mixture toward the centre of pan; tilt the pan, allowing the uncooked egg mixture to run onto the base of the pan. Repeat about four times around the pan, until the egg is just set. Fold one side of the omelette over using the spatula. Slide onto a plate.
Repeat, wiping out pan with paper towel before each addition, to make a total of 4 omelettes. Serve as is or with your favourite filling.