Heat 1-inch of vegetable oil on medium-high in a deep pan.
While vegetable oil is heating, mix eggs, sugar, vanilla and milk until well blended.
Slowly add the flour, salt and baking powder, stirring well.
Test the temperature by dropping a pinch of flour into the hot oil. If it sizzles right away without smoking, it's perfect. If you suffer 3rd degree burns from the backsplash it's probably too hot.
Using a funnel or even a ladle, drop mixture into hot oil working from center outwards in a web pattern. (You can use a gallon sized freezer bag instead of a funnel by pouring the batter into the bag, snipping off a small corner of it, and squeezing the batter into the oil.)
Using a pair of kitchen tongs, quickly turn the funnel cake over as soon as one side is golden brown.
After the other side has cooked, remove it from the oil and place it on top of a paper towel-lined plate.