Put cleaned leeks in a pot of water over medium-low heat, cover and cook until soft (they should be tender when poked with a spoon). Drain the leeks and allow to cool. Squeeze out as much as liquid as possible. Put the leeks in a food processor and blend until smooth. Mix in the egg, salt and breadcrumbs. The mixture should be quite soft but just firm enough to form into patties. Put about 1 cm oil in a pen over medium heat. Form the leek mixture into small patties and carefully drop in the oil. Fry until evenly browned and crispy on both sides. Transfer to paper towel-lined plate. Serve immediately. Variation: Leek patties are also very popular during Passover. To make them kosher for Passover, simply swap the breadcrumbs for matzo meal. TIP: To clean leeks, cut in half lengthwise and rinse thoroughly, then soak in a solution of water and a little distilled vinegar. The vinegar will draw the dirt out of the leeks.