Cucumbers become meltingly tender when cooked, with a flavor similar to yellow squash. Kirby cucumbers, the kind typically used for pickles, are crisp and unwaxed, allowing you to leave a little of the skin on which brings additional texture and color to the finished dish. Choose cucumbers that are firm, without any bruises or blemishes, and not too large. The larger the cucumber, the seedier it tends to be. Leeks lend a delicate onion note. To clean the leeks, cut them first and then soak in several changes of cold water until no grit remains.
Add 1/4 cup of water and the remaining 1/2 tablespoon butter and cover the pan. Cook until the cucumbers are crisp-tender, 3 minutes. Uncover the pan, raise the heat to medium, add the dill and cook until the liquid has almost evaporated, 2 to 3 minutes more.