Beat together eggs and water until blended. In a 10-inch omelet pan heat butter until just hot enough to sizzle a drop of water. Pour in egg mixture. Mixture should set immediately at edges. With an inverted pancake turner, carefully push cooked portions at edges toward center so uncooked portions can reach hot pan surface, tilting pan and moving as necessary. Continue until the egg is set and will not flow.
Fill the omelet with 1/2 cup of desired mixture. With a pancake turner, fold omelet in half. Invert onto plate and serve immediately.