Cut the flesh from the melon and cut into bite size pieces, removing and discarding the seeds, and set aside. Peel and halve the onion, and thinly slice.
In a small bowl, combine the vinegar, salt, pepper, and whisk until salt is dissolved. Slowly whisk in the olive oil, a few drops at a time. Add in the chopped mint, taste, and adjust seasonings.
In a large bowl, combine the melon, onion, and feta. Pour the dressing over the melon mixture and toss gently until everything is coated and evenly mixed. Garnish with mint sprigs.