To prepare the leeks, cut the root and the tip off. Slice each leek lengthwise, and wash under running water between the leaves to remove any extra grit. Dry the leeks, and cut them into bite-sized pieces.
Heat a large pan, and melt one tablespoon of butter over medium-high heat.
Add the leeks to the pan, and toss to coat in the butter. Add salt, and stir.
Reduce heat to medium-low, and allow to cook until the leeks are extremely tender, about 35-40 minutes. Stir occasionally.
Remove the pan from the heat, and add the remaining tablespoon of butter. Stir into the leeks until it is fully melted and the butter has formed a sauce.
Transfer the leeks to a serving dish, and serve with a large serving spoon.
Pro-tip: Cook the leeks a little longer for a fantastic warm relish or salsa to put on top of grilled chicken or fish.