Heat butter or margarine on low in a medium-size pan and sauté apples for 5 minutes.
Mix together brown sugar and cinnamon. Sprinkle over apples. Toss and continue to sauté apples for 10 minutes, until they caramelize. The mixture will be thick and syrupy.
Spoon mixture into an 8X8-inch baking dish and place in a 450°F oven.
Separate eggs. Whisk yolks and granulated sugar in a small bowl until fairly thick. In a large bowl, beat egg whites with cream of tartar until stiff and shiny.
Fold whites into yolk mixture, a third at a time. Pour egg mixture over the apples and bake for 8 to 10 minutes.
Remove from oven. The omelet will be puffed and golden. Sprinkle with confectioners sugar, and serve immediately.