Unfold puff pastry on a lightly floured surface. Roll pastry into a 14-inch square. Using a knife, cut pastry into four 7-inch squares. Set aside.

Preheat oven to 375F. Peel and core apples. If necessary, trim bottoms of apples so they stand upright. Place an apple in the center of each pastry square. In a small bowl stir together sugar and cinnamon; spoon into centers of apples.

In another small bowl beat egg and the water with a fork. Moisten the edges of the pastry squares with egg mixture; fold corners to center over apples. Pinch to seal, pleating and folding pastry along seams as necessary. Place dumplings in a 13x9x2-inch baking pan. Using a pastry brush, brush dumplings with egg mixture.

Bake dumplings, uncovered, in the preheated oven for 30 to 35 minutes or until apples are tender and pastry is golden. (Test for doneness by sticking the tip of a paring knife into a dumpling.) Meanwhile, combine caramel topping and pecans in a microwave-safe 2-cup glass measure; microwave, uncovered, on 100-percent power (high) for 30 to 60 seconds or until heated through, stirring once. Serve dumplings warm with sauce. Makes 4 dumplings.

Apple Dumplings with Cranberry-Sour Cream Filling: Prepare apples as above, except omit the cinnamon and sugar. In a small bowl combine 2 tablespoons sour cream, 2 tablespoons packed brown sugar, 2 tablespoons dried cranberries, 2 tablespoons chopped toasted pecans, and, if desired, 1/2 teaspoon grated orange peel. Fill apples with sour cream mixture.