Stir together salt, honey, and vinegar. Add the shallot slices, making sure that they’re all submerged. Set aside.

Wrap the beets in foil and bake at 400° for about an hour, until they can be pierced easily with a toothpick. When they are cool enough to handle, slip off the skins and slice them.

Pour the vinaigrette and shallots over the beets and stir well. Sprinkle on the mint and stir again, then let sit at least two hours. If prepared in advance, chill, then allow to come to room temperature before serving.