In an 8 inch ( 20 cm) non stick skillet with sloping sides, melt butter over medium heat. Add apple slices in a layer. Cook 2 minutes. Sprinkle with1 tsp (5 ml) sugar and cinnamon, to taste. Cook until tender, 3 to 5 minutes longer. In a small bowl, combine eggs, 1 tsp (5 ml) sugar and water. Beat with a fork until eggs are just blended. Pour over apples in skillet. Stir with a spatula to allow egg mixture to cover bottom of pan. Use spatula to gently push cooked portions to the center, tilting skillet to allow uncooked egg to flow into empty spaces. When egg is almost set on surface, sprinkle cheese over half of omelette. Slip spatula under unfilled side, fold over filling and slide onto serving plate. Sprinkle with cinnamon or icing sugar, if desired, and serve immediately.