Preheat oven to 400°F (200°C). In a medium saucepan, bring butter, water, and vanilla extract to a boil over medium-high heat. Add flour all at once, stirring vigorously until a dough forms. Remove from heat and cool slightly. Beat in eggs one at a time until smooth and glossy.

Drop tablespoon-sized mounds of dough onto a parchment-lined baking sheet, spacing 2 inches apart. Bake for 25-30 minutes, until golden brown and crisp. Cool completely on a wire rack.

In a large bowl, combine heavy cream, instant vanilla pudding mix, and milk. Beat with an electric mixer on high speed until stiff peaks form, about 2-3 minutes.

Slice cooled pastry shells in half horizontally. Fill with vanilla cream and place the top half back on. Dust with powdered sugar.