Combine water and butter in a small saucepan, bring to a boil, then reduce heat. Add flour and stir with a wooden spoon. Stir until the mixture leaves the sides of the pan. Add the eggs, one at a time, beating well after each addition. Drop by teaspoonful onto ungreased cookie sheet and bake at 400 degrees for 40 minutes. Reduce temperature to 350 degrees and bake for 15 minutes or longer, until puffs are firm to the touch. Loosen them from the cookie sheet and cool on a wire rack. Prepare 1 large box of vanilla pudding pie filling according to the pie filling directions. When puffs are cool, use an icing tube and squeeze about 1 Tablespoon of pudding into each pastry puff. Refrigerate for 1 hour and serve.
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