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. Place in a medium bowl with cold water for about 5 minutes to allow any excess dirt to fall to the bottom of the bowl. Dry the leek rings on a clean kitchen towel or several layers of paper towels.
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 lined with paper towels Season with additional salt and serve immediately.