This classic cream puff dessert is easily made ahead. Bake the shells up to a month in advance, then freeze in an airtight container. Several hours before serving, cut top third off puffs using a serrated knife. Fill the frozen shells with the custard filling and refrigerate. In the refrigerator, the shells will thaw but remain crisp.
To prepare filling, heat 1 1/4 cups milk in a medium, heavy saucepan to 180° or until tiny bubbles form around the edge (do not boil). Combine remaining 1/4 cup milk, 1/4 cup granulated sugar, cornstarch, 1/8 teaspoon salt, and 2 eggs in a medium bowl, stirring well with a whisk. Gradually add the hot milk to the sugar mixture, stirring constantly. Place milk mixture in pan. Add 1 teaspoon butter; cook over medium heat until thick and bubbly (about 3 minutes), stirring constantly. Reduce heat to low, and cook 2 minutes, stirring constantly. Strain mixture through a sieve into a bowl; stir in vanilla. Place plastic wrap directly on surface of custard; refrigerate 2 hours or until chilled. Fold in whipped topping. Cover and chill.
Preheat oven to 425°.
To prepare shells, cover a large, heavy baking sheet with parchment paper. Combine water, 3 tablespoons butter, 2 teaspoons granulated sugar, and 1/4 teaspoon salt in a large, heavy saucepan over medium-high heat, stirring occasionally with a wooden spoon. Bring to a boil; remove from heat. Lightly spoon flour into a dry measuring cup; level with a knife. Add flour to water mixture, stirring well until smooth and mixture pulls away from sides of pan. Return pan to heat; cook 30 seconds, stirring constantly. Remove pan from heat. Add 2 eggs and egg whites, 1 at a time, beating with a mixer at medium speed just until combined. Beat 1 minute at medium speed.
Drop the dough into 10 mounds (about 1/4 cup each), 2 inches apart, onto prepared baking sheet. Bake at 425° for 20 minutes; reduce oven temperature to 350° (do not open oven door). Bake an additional 20 minutes. Turn oven off, and partially open oven door. Pierce the top of each puff with a knife; cool puffs in oven 20 minutes. Remove from oven; cool completely on a wire rack.
Cut top third off puffs; fill each puff with about 1 tablespoon filling. Replace tops, and sprinkle with powdered sugar.
Note: A small rubber spatula is the best tool for releasing the sticky cream puff dough onto the baking sheet.