In a large, thick-bottomed skillet, pour oil to about 2 inches deep. Preheat over medium-high heat while you make the batter.
In a large mixing bowl with a hand mixer, beat eggs, sugar, milk, flour, baking powder, and salt until smooth.
Test your oil by dropping a tiny sprinkling of flour into it. If the flour sizzles, the oil is hot enough and test at 370-375F (187-190C) using a thermometer. Once it tests hot enough, turn the temperature down to medium.
The portion about ½ cup of batter into a measuring cup. Slowly drizzle batter into oil in a thin stream, swirling and crisscrossing the batter over itself.
Fry on each side until golden brown (about 90 seconds per side) then remove to a paper-towel-lined plate.
Dust with powdered sugar and serve warm.
Repeat with remaining batter but make sure that oil returns to temperature in between batches.