Preheat the oil in a heavy 5-quart pot over medium-high heat to 375 degrees F.
Slice the leeks into 1/2-inch wide rings, separating them 2 layers at a time.
In a medium mixing bowl, whisk together the milk and the egg. In another medium mixing bowl, combine the flour and salt. Divide the flour into 2 separate, shallow dishes and place the milk and egg mixture in a third. Going 1 small handful at a time, dip 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 for 1 to 1 1/2 minutes, or until golden brown. Remove the rings to a cooling rack set inside a half sheet pan and allow to drain for 2 to 3 minutes before serving. Season with additional salt, if desired.