Preheat oven to 425°F (220°C). Line two baking sheets with parchment paper and set aside.

In a medium saucepan, combine water, butter, and salt. Bring to a full rolling boil over medium-high heat, ensuring the butter melts completely.

Remove from heat and add all the flour at once. Stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the pan sides, about 1 minute. Return to low heat and stir for 30 seconds to cook out excess moisture.

Transfer the dough to a large bowl and let cool for 3 minutes. Add eggs one at a time, beating well after each addition until the dough is smooth and glossy. The consistency should be thick but pipeable.

Transfer dough to a piping bag fitted with a 1/2-inch round tip. Pipe 1.5-inch mounds onto prepared baking sheets, spacing them 2 inches apart. Smooth any pointed tops with a wet finger.

Bake for 15 minutes at 425°F, then reduce heat to 375°F (190°C) without opening the door. Continue baking for 20-25 minutes until deep golden brown and crisp. Turn off oven, poke a small hole in the bottom of each puff with a skewer, and leave in the oven for 10 minutes to dry out.

For the pastry cream, whisk together milk and half the sugar in a saucepan over medium heat until steaming. In a bowl, whisk egg yolks, remaining sugar, and cornstarch until pale. Slowly pour half the hot milk into the yolk mixture while whisking, then pour everything back into the saucepan.

Cook over medium heat, whisking constantly, until the mixture thickens and bubbles, about 2-3 minutes. Remove from heat and whisk in butter and 1 teaspoon vanilla. Strain through a fine-mesh sieve into a bowl, press plastic wrap directly on the surface, and refrigerate until completely cold, at least 2 hours.

Beat heavy cream, powdered sugar, and remaining 1 teaspoon vanilla to stiff peaks. Whisk the chilled pastry cream until smooth, then fold in the whipped cream until evenly combined.

Fill a piping bag with the vanilla cream and pipe into each puff through the bottom hole until slightly resistant. Dust generously with powdered sugar just before serving.