Fill a Dutch oven or heavy-bottomed pot with at least 2 inches of vegetable oil and place over medium heat. Heat the oil to 300 degrees F.
While you wait for the oil to come up to temperature, combine all of the other ingredients (except the powdered sugar) in a small saucepan over very low heat. Whisk together the ingredients until a smooth batter forms. Turn the heat off and let the batter rest until the oil is ready. Line a baking sheet with a double layer of paper towels and set aside.
Once the oil reaches 300 degrees F, use a medium cookie scoop to scoop the batter and drop into the oil. Don't overcrowd the pot, ensuring that each zeppole has enough space to fry. Once the bottom side is golden brown, gently flip the zeppole over and continue frying until the other side is golden brown. This should take anywhere from 5 to 8 minutes total. Remove the zeppole with a slotted spoon or spider strainer and place on the paper towel-lined baking sheet. Allow the oil to return to 300 degrees if the temperature has dropped, and continue frying, using the rest of the batter.
Dust the zeppole with powdered sugar and serve warm or at room temperature. The zeppole are best eaten the same day they are made.