Fresh cucumbers are excellent when gently braised in butter and served warm. This dish is best with thin-skinned cucumbers, like English, Japanese and Persian varieties.
In a large skillet, melt 1 tablespoon of the butter. Add the leek and cook over moderately low heat, stirring, until tender, 4 minutes. Stir in the cucumbers, the remaining 1/2 tablespoon of butter and the water. Season with salt. Cover and cook over moderate heat, stirring a few times, until the cucumbers are crisp-tender, 3 minutes. Uncover and cook over moderately high heat until any liquid has evaporated, about 1 minute. Transfer the cucumbers to a bowl, stir in the dill and serve.