Step 1: In a medium saucepan, combine water, butter, sugar, and salt. Bring to a boil over medium heat.
Step 2: Reduce heat to low and add flour all at once. Stir vigorously with a wooden spoon until mixture forms a ball and pulls away from the sides of the pan.
Step 3: Remove from heat and let cool for 5 minutes. Transfer dough to a mixing bowl.
Step 4: Using an electric mixer on medium speed, add eggs one at a time, beating well after each addition until fully incorporated.
Step 5: Mix in vanilla extract until dough is smooth and glossy.
Step 6: In a deep pot or Dutch oven, heat 2 inches of vegetable oil to 375°F (190°C).
Step 7: Drop tablespoon-sized portions of dough into the hot oil, frying 4-5 at a time without crowding.
Step 8: Fry for 3-4 minutes, turning occasionally, until golden brown and puffed.
Step 9: Remove with a slotted spoon and drain on paper towels.
Step 10: Dust generously with powdered sugar while still warm. Serve immediately.