In a saucepan, bring the butter and water to a simmer. When the butter has melted, take off the heat and whisk in all the flour. Return to the heat and stir vigorously over a gentle flame for a minute or two, until the dough forms a smooth ball.
Turn the dough into the bowl of a standing mixer, spread it out over the bottom and sides with a spoon or spatula to speed cooling. Let it cool completely.
Place the bowl on the standing mixer with the whisk attached. Set the speed to medium and add the beaten eggs to the bowl one by one. Continue whisking the eggs into the dough until it obtains a smooth, thick paste-like consistency.
Fill a pastry bag with a star tip with the dough. On a baking sheet lined with parchment paper or a silicone baking mat, pipe doughnut shaped swirls of the dough about 8-10cm (3-4 inches) wide. Go round twice so that each zeppola has two layers of pastry.
Bake your zeppole at 200C/400F for 25-30 minutes, or until they are cooked through and golden brown.
Place them on a rack and let them cool complete