Beat the egg whites and the cream of tartar in a large, clean bowl with clean beaters (or a wire whisk) until soft peaks form. Add the vanilla and sugar, and beat until the sugar dissolves and the resulting meringue is stiff.
Beat the egg yolks and the Cointreau with 1/4 cup water, until thick and lemon-colored. With a rubber spatula, stir in the flour until no dry flour is visible.
Fold the meringue into the egg yolk batter with a rubber spatula. Stir only until the mixture is evenly blended. Streaks are okay.
Rub a very clean round-bottomed skillet or omelette pan with butter. (Or use a non-stick pans.) Pour small pancake-size round disks or ovals into the pan. Put the pan into the oven for eight to ten minutes, until puffy and lightly browned. You can do more than one at a time, but don’t open the oven while they’re in there.
Meanwhile, peel and section the oranges. If the sections are large, you can slice them across.
Remove the omelettes from the pans. Spoon some of the orange sections into half of the omelettes, and fold them over. Garnish with more orange sections and powdered sugar.
Strain the orange juice into a small saucepan over medium heat. Dissolve the sugar into it and bring it up to a light boil. Reduce by half.
Remove the pan from the heat and stir in the dissolved cornstarch. Sprinkle in the orange zest, and serve in ribbons over the omelettes.
