Beat the eggs, milk, and vanilla together in a large bowl until well mixed.
In a medium bowl whisk together the flour, sugar, baking powder, and salt.
Pour the flour mixture into the egg mixture and whisk together until there are no visible lumps.
Heat the oil to 375 degrees F in a deep cast-iron skillet or a pot. (If you don't have a candy thermometer, a wooden spoon or tooth stick will show bubbles when stuck into the oil when the temperature is hot enough.)
Cover the spout of a funnel with your finger and pour 1 ladle of batter into it. Remove your finger and move the funnel in a spiral motion over the hot oil until all of the batter is released.*Be careful not to hold the funnel too high above the oil or you might end up with several tiny and too thin dough strings. Hold it relatively close to the oil and try to connect the dough strings with your movements. The dough will start to move outward from the middle toward the rim of the pot. Just keep spreading the dough in a circular motion and the single pieces will come together (most of them).
Fry for 90 seconds to 2 minutes on each side, or until golden brown.
Transfer the cooked funnel cake to a paper towel-lined baking sheet to absorb any excess oil. Repeat with the remaining batter.
Once cooked, dust the funnel cakes with powdered sugar and serve warm.