In a large skillet, melt 1 tablespoon of the butter over medium-low heat. Add the leeks and cook, stirring occasionally, until tender, 3 to 5 minutes. Add the cucumbers, season with salt and toss to coat.
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.