In a large mixing bowl, whisk together eggs, milk, water, and vanilla extract until smooth.
In another bowl, combine flour, sugar, baking powder, and salt.
Gradually add dry ingredients to the wet mixture, whisking until smooth. The batter should be pourable.
Heat about 2 inches of oil in a large skillet or saucepan to 375°F (190°C).
Cover the spout of a funnel with your finger, pour in 1/2 cup batter, then release into hot oil in a circular motion.
Fry until golden brown on one side (about 1 minute), flip, and cook the other side for another minute.
Remove with tongs and place on paper towels to drain.
Dust generously with powdered sugar and serve warm.