Prepare the pastry:

1. Preheat your oven to 425°F (220°C).
2. In a medium saucepan, combine the butter and water and bring to a boil.
3. Add the flour all at once and stir vigorously with a wooden spoon until the mixture forms a smooth ball that pulls away from the sides of the pan.
4. Remove from heat and let the mixture cool for about 5 minutes.
5. Beat in the eggs one at a time, making sure each egg is fully incorporated before adding the next.
6. Drop the dough by tablespoonfuls onto an ungreased baking sheet, forming about 12 mounds. Make sure to space them apart as they will expand during baking.

Bake the pastry:

1. Place the baking sheet in the preheated oven and bake for 20-25 minutes, or until the puffs are golden brown and puffed.
2. Remove the puffs from the oven and transfer them to a wire rack to cool completely. You can prick each puff with a knife to release steam and prevent them from getting soggy.

Prepare the filling:

1. In a mixing bowl, whip the heavy cream with an electric mixer until it begins to thicken.
2. Add the powdered sugar and vanilla extract to the cream. Continue whipping until the cream forms stiff peaks.

Assemble the cream puffs:

1. Once the pastry shells are cool, use a serrated knife to gently cut the tops off each puff.
2. Spoon or pipe the whipped cream into the bottoms of the pastry shells.
3. Replace the tops onto the filled shells.

Dusting and serving:

1. Just before serving, dust the cream puffs with powdered sugar.
2. Serve immediately, or keep them refrigerated until ready to serve.