Combine 1/2 teaspoon of sugar with the cinnamon. Place the fruit in a small bowl, and the cinnamon-sugar. Toss to combine.
Heat 3 tablespoons butter in a small saute pan over medium heat. Add the fruit, and saute for about 5 minutes or until fruit begins to caramelize. Remove from the heat, and set aside.
Preheat the over to 375. Using an electric mixer, beat the egg white until stiff peaks form. Using the electric mixer again, beat the egg yolks with the remaining sugar until very light, and fluffy. Fold in the vanilla, and lemon zest. When well blended, fold in the beaten egg whites.
Pour the melted butter into a 7-inch, ovenproof omelette pan over medium heat. Place the fruit(if sliced, fan it out) into the pan and pour the batter to cover the fruit. Cook for 1 and half minutes. Place in the preheated over and bake for about 10 minutes or until omelette is puffed and golden. Remove from the oven and carefully invert into a serving plate. Dust with confectioners' sugar, and serve.