Preheat oven to 400°F (200°C). In a saucepan, bring water, butter, and salt to a rolling boil. Reduce heat to low, add all the flour at once, and stir vigorously until a smooth dough ball forms that pulls away from the pan sides. Remove from heat and cool for 5-10 minutes.

Transfer the dough to a mixer bowl. Add eggs one at a time, beating well after each addition until the dough is thick, smooth, and glossy.

Transfer dough to a piping bag with a large round tip. Pipe 1.5-inch mounds onto parchment-lined baking sheets. Smooth down any peaks with a wet finger.

Bake for 30-35 minutes until deep golden brown. Do not open the oven for the first 25 minutes. Turn off the oven, poke a small hole in the side of each puff to release steam, and cool completely in the oven with the door ajar.

Heat milk until simmering. In a separate bowl, whisk sugar, cornstarch, salt, and egg yolks until smooth. Slowly whisk in about half of the hot milk to temper. Pour the tempered mixture back into the saucepan.

Cook over medium heat, whisking constantly, until the cream thickens and boils for one minute. Remove from heat, stir in butter and vanilla. Strain through a fine-mesh sieve, cover with plastic wrap pressed directly onto the surface, and refrigerate until fully chilled (at least 2 hours).

Once shells and cream are cool, slice the puffs in half and spoon or pipe the filling inside. Dust with powdered sugar or drizzle with melted chocolate before serving.