Like onions, leeks develop a rich, savory flavor when cooked slowly. And when cooked this way, they make an excellent addition to a creamy mound of mashed potatoes.
Rather than caramelize the leeks, which requires a bit more hands on cooking, we decided to melt them. It's actually a braise, but the result is meltingly good. And braising requires only an occasional stir. The leeks are thinly sliced, then slowly simmered in broth or stock until extremely tender, then the whole mixture is stirred into the potatoes.
The easiest way to clean leeks is to cut them up first. Trim off the ends, cut them in half lengthwise, then thinly slice them. Place the slices in a large bowl of cool water and toss well, separating the layers, to rinse away any dirt. Allow the dirt to fall to the bottom of the bowl, then use a slotted spoon to scoop out the floating leeks.