Prepare the Oil:
In a deep pot or Dutch oven, heat 2–3 inches of vegetable oil over medium heat until it reaches 350°F (175°C).
Make the Dough:
In a medium saucepan, combine water, butter, sugar, and salt. Bring to a boil.
Once boiling, reduce heat to low, add flour all at once, and stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides (about 1–2 minutes).
Cool and Add Eggs:
Transfer dough to a mixing bowl and let it cool for 5 minutes.
Beat in eggs one at a time, fully incorporating each before adding the next. Stir in vanilla extract and lemon zest. The dough should be smooth and sticky.
Fry the Zeppole:
Using a small cookie scoop or spoon, drop about 1 tablespoon of dough at a time into the hot oil.
Fry in batches for 3–4 minutes, turning occasionally, until puffed and golden brown.
Remove with a slotted spoon and drain on paper towels.
Dust and Serve:
While still warm, generously dust with powdered sugar. Serve immediately.