Combine the water, milk, butter, sugar, and salt in a medium saucepan. Set over medium heat and bring to a boil.

Move the pan briefly off the heat. Add all of the flour at once and stir until combined.

Return the pan to medium heat and cook, stirring constantly, for about 1 1/2 minutes to release as much moisture as possible. The dough should pull together into a smooth mass.

Transfer the dough to the bowl of a stand mixer fitted with the whisk attachment. Beat on medium speed until the dough has cooled and no more steam is coming off.

Add the eggs one at a time, mixing until each egg is fully incorporated before adding the next. Continue until the batter is thick and smooth.

Heat several inches of neutral oil in a wok or deep, heavy-bottomed pot to 350°F (175°C).

Using two spoons, scoop and shape small portions of batter and carefully drop them into the hot oil. Fry in batches, turning the zeppoles so they brown evenly, until deeply golden and puffed.

Remove the zeppoles from the oil and drain briefly.

Put the warm zeppoles in a brown paper bag with a generous amount of powdered sugar. Close the bag and shake until thoroughly coated. Serve warm.