Preheat the oven to 400°F and line 2 baking sheets with parchment paper.

In a medium saucepan over medium heat, combine the butter, water, sugar, and salt. Bring to a simmer until the butter is melted.

Add the flour all at once and stir vigorously for 1 to 2 minutes until the dough forms a ball and pulls away from the sides of the pan.

Transfer the dough to a mixing bowl and let it cool for 5 minutes.

Beat in the eggs one at a time until the dough is smooth, glossy, and thick.

Drop or pipe 12 mounds of dough onto the prepared baking sheets, spacing them evenly apart. Smooth any peaks with a damp fingertip.

Bake for 20 minutes. Reduce the oven temperature to 350°F without opening the door and bake 12 to 15 minutes more, until deeply golden and dry.

Remove from the oven, poke a small hole in each puff to release steam, and cool completely on a rack.

In a large bowl, whisk together the cold heavy cream, milk, instant vanilla pudding mix, and vanilla extract until thick and fluffy. Chill for 10 to 15 minutes if needed for a firmer consistency.

Slice the cooled puffs in half or make a small opening for piping. Fill each puff generously with the vanilla cream.

Dust with powdered sugar just before serving.