Heat the oil in a 5-quart Dutch fitted with a deep-fry thermometer oven over medium-high heat to 375ºF.
Slice the leeks into 1/2-inch wide rings, separating them 2 layers at a time.
Whisk together the milk and the egg in a medium mixing bowl. Combine the flour and salt in another medium mixing bowl. Divide the flour into 2 separate, shallow dishes and place the milk and egg mixture in a third.
Dip one small handful of the rings first into the first flour mixture, then into the milk and egg, and then into the second flour mixture. Working in batches, fry the rings until golden brown, 1 to 1 1/2 minutes. Using a spider strainer, carefully remove the rings to a wire rack set inside a half-sheet pan and drain for 2 to 3 minutes before serving. Season with additional salt, if desired.