Coffee Liqueur Apple Pie

In a saucepan, heat 1/2 cup apple juice and 1/2 cup sugar. Add the apples and cook gently, covered, until almost tender. Remove with a slotted spoon and set aside. Add 1/2 cup coffee liqueur to the cooking liquid. If the liquid measures less than 1-1/4 cups, add more apple juice. Over medium heat, add 1 tablespoon butter. Blend 1-1/2 tablespoon cornstarch with 1 tablespoon lemon juice. Stir into the liquid, cooking until the sauce thickens. Remove from the heat and add the apples. Turn into unbaked pie shell. Cover with top pastry, seal, and flute the edges. Prick the top crust or cut small decorative patterns. Brush the top lightly with 1 tablespoon melted butter and sprinkle with 2 tablespoons sugar. Bake on the lower rack, below the oven center, for 25 to 30 minutes, or until golden brown.