In a small bowl combine eggs, the water, the salt, and pepper. Beat with a fork until combined but not frothy. For omelet, in an 8-inch nonstick skillet with flared sides heat 1 tablespoon of the butter over medium-high heat until melted. Pour half of the egg mixture into skillet. Cook over medium heat. As mixture sets, run a spatula around edges of skillet, lifting egg mixture so the uncooked portion flows underneath. Continue cooking and lifting edges until egg mixture is set but is still shiny. Lift and fold one edge of the omelet to the opposite edge. Gently slide omelet out of skillet onto a warm plate. Cover with foil; keep warm. Repeat to make a second omelet, using the remaining 1 tablespoon butter and the remaining egg mixture.