Thinly slice the white and light green parts of the leek into 3-inch-long julienne strips. Rinse in a bowl of water to remove the grit, drain, and pat dry.
In a small (2-quart) saucepan) heat the oil over medium-high heat (it should reach a depth of about 1 inch) until it's between 325º and 350ºF on a candy thermometer. Reduce the heat to medium or medium-low to hold the oil in this temperature range.
Add a small handful of the leeks to the oil. (Caution: the oil will bubble up immediately. Always fry in small batches to avoid overcrowding the pan and to prevent boil-overs.)
Fry the leeks, stirring often with a metal slotted spoon, until the oil is barely bubbling and the leeks are light golden brown, 1 to 3 minutes. (The oil temperature will drop when you add the leeks; let it return to the starting temperature before frying the next batch.)
Lift the leeks from the oil using the slotted spoon, tap against the side of the pan to drain off excess oil, and transfer to a large plate lined with a couple of layers of paper towel. Gently shake on the paper towel and then slide the leeks onto the paper towel below it, discarding the oil-soaked top layer.
Sprinkle the leeks lightly with salt while they're still hot. Let cool to room temperature before using as a garnish.
The leeks can be stored for a few days in a sealed container, but they'll taste their best when made no more than 4 hours ahead.