Peel and slice two of the cucumbers. Peel, seed and grate the remaining cucumber. Heat the butter in a large, heavy saucepan. Add the sliced cucumbers and cook over low heat for a few minutes.
For the relish, quarter the cucumber lengthways, then thinly slice and place in a bowl along with the onion. Season with a few generous pinches of salt. Mix well and leave to rest for 15 minutes.