Shallots: Slice the shallot and pour the vinegar over it. Set aside.

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

Stir together salt, honey, and vinegar; pour over the beets and stir well. Sprinkle on the mint and stir again. Let sit at least two hours. If prepared in advance, chill, then allow to come to room temperature before serving.

Nuts: Combine the sugar and water in a small saucepan and cook over medium-high heat, swirling occasionally, until the sugar turns a golden amber color, 3 to 4 minutes. Add the nuts and stir to coat. Continue cooking until nuts are fragrant and golden brown, about 1 minute. Transfer to sheet of parchment, spread into a thin layer, and cool completely.

Vinaigrette: Whisk together the rhubarb, mustard, salt, sugar, and vinegar. Slowly beat in the oil to emulsify. Cover and refrigerate.

Salad: Toss the arugula with enough vinaigrette for the greens to be lightly coated. Scoop the shallots out of the vinegar and add them along with the nuts and cheese; toss gently. Arrange the beet slices on top of the salad, and serve.