Drain artichoke hearts, reserving 2 tablespoons of the liquid. In a bowl combine artichoke hearts, onion, sweet pepper, and ham; toss with the reserved liquid. Heat a skillet over medium-high heat. Add artichoke mixture to skillet. Cook and stir about 6 minutes or until ham and vegetables begin to char. Remove from heat; set aside.
Meanwhile in a bowl combine eggs, water, salt, and pepper. Beat mixture with a fork or rotary beater until frothy. Heat a 12-inch nonstick skillet with flared sides over medium-high heat. Add butter to skillet; melt, swirling to coat pan. Add egg mixture; reduce heat to medium. Stir egg mixture gently but continuously until mixture resembles small pieces of cooked egg surrounded by liquid egg. Stop stirring. Cook 30 to 60 seconds more or until egg is set but shiny.
Spoon filling mixture onto one half of the omelet. With a spatula, lift and fold opposite side over filling. Invert onto a serving plate. Gently cut in two. Makes 2 servings.