Heat the oven to 425°F and line one or two baking sheets with parchment paper.

Combine the water, whole milk, butter, granulated sugar, and salt in a medium saucepan. Bring the mixture to a full simmer over medium heat, stirring until the butter has completely melted.

Add the flour all at once and stir vigorously with a wooden spoon until a smooth dough forms and pulls away from the sides of the pan.

Continue stirring the dough over medium-low heat for 1 to 2 minutes, until it looks smooth and a thin film forms on the bottom of the saucepan.

Transfer the dough to a mixing bowl and let it cool for about 5 minutes. Add the eggs one at a time, beating thoroughly after each addition until the dough is smooth, glossy, and thick enough to hold a soft peak.

Pipe or scoop mounds about 1 to 1 1/4 inches wide onto the prepared baking sheets, leaving about 2 inches between them. Smooth any pointed tops with a damp fingertip.

Bake at 425°F for 10 minutes, then reduce the oven temperature to 375°F and bake for another 10 to 15 minutes. Do not open the oven during the first 20 minutes; bake until the puffs are deeply golden and firm.

Turn off the oven, crack the door open, and leave the puffs inside for 5 to 10 minutes. Transfer them to a rack and cool completely before filling.

Beat the cold heavy cream, confectioners’ sugar, and vanilla extract until medium-stiff peaks form. Split each cooled puff horizontally or make a small opening in the side or bottom, then pipe in the whipped cream.

Dust the filled puffs with confectioners’ sugar or drizzle them with melted chocolate before serving.