Warm 1 cup milk in a saucepan. Whisk 3 tbsp sugar, cornstarch, and egg yolks in a bowl. Temper with hot milk, return to pan, and whisk over medium heat 2 minutes until thick. Stir in vanilla, cover with plastic wrap, and chill.

Heat oven to 400°F. Boil 1/2 cup milk, water, butter, 1 tbsp sugar, and salt. Add flour all at once and stir over low heat for 60 seconds until a smooth ball forms. Cool 3 minutes.

Beat in eggs a quarter at a time until the dough falls from the spoon in a V shape. Pipe 12 mounds onto a parchment-lined sheet and tap down peaks.

Bake at 400°F for 15 minutes, lower to 350°F and bake 15 minutes more until deep golden. Turn off oven, crack door, and leave puffs inside 20 minutes. Poke a steam hole in each.

Whisk chilled custard smooth and pipe into the steam hole of each puff until slightly heavy.

Pile onto a plate, dust with powdered sugar, and serve within a few hours.