To make the dough, combine water, butter, and salt in a medium saucepan and bring to a boil over medium heat.
Once boiling, add the flour and sugar all at once and stir vigorously with a wooden spoon until the mixture forms a ball and pulls away from the sides of the pan. Cook the flour paste until it forms a ball, leaves a thin film on the pan, and steams heavily for about 1–2 minutes.
Remove the saucepan from the heat and let it cool for 10 minutes.
Add the eggs, one at a time, mixing well after each addition until fully incorporated. I use a hand mixer for this. The dough should be smooth and shiny.
Transfer the dough to a piping bag fitted with a large star tip and let the dough cool about 10 minutes before piping.
Heat vegetable oil in a large pot or deep fryer to 350°F (175°C).
Pipe small rounds of dough (~3 to 3.5-inch circles) onto the parchment-paper-lined baking sheet, leaving some space between each one to allow for expansion during frying. The large open star tip, such as Ateco 828 or 829 (or Wilton 1M), creates defined ridges that help the choux hold its shape and puff evenly.
Carefully transfer the parchment paper with the piped zeppole into the hot oil, with the parchment paper side up. The zeppole will easily detach from the paper as they fry.
Fry the the zeppole until golden brown and puffed up, about 3-4 minutes per batch. Turn them halfway through cooking to ensure even browning.
Transfer them to a wire rack to drain so steam doesn’t soften the shells; if you’d like them extra crisp, place the fried pastries in a 300°F (150°C) oven for 5–8 minutes to dry them further.