Prepare the leek by cutting off the roots, then peeling off the outermost leaf.
Slice the leek thinly until you’ve gotten through the white and very pale green stalk, and are approaching the point where the leaves turn dark and split off.
Measure the sliced leeks; you should have approximately 2 cups per leek. (Don’t worry about being super precise, but if you have significantly more or less, adjust the salt and butter accordingly.)
Wash the leeks very well under cool running water. Use your fingers to break up the ringed segments so that each strand is separate.
Melt the butter in a large pan on medium heat. Once it’s melted, add the salt and stir.
Add the leeks into the pan, then turn the heat up to high.
Cook the leeks on high for 3-4 minutes, stirring constantly, until they soften.
Reduce the heat to low and cook uncovered for about 45 minutes, stirring occasionally. By the end of this time, the leeks will be meltingly soft and delicious.