Line a baking sheet with parchment paper or a silicone baking liner. Preheat the oven to 425.
Whisk the vinegar, shallots, and honey in a medium bowl. Gradually whisk in the oil. Season the vinaigrette with salt and pepper.
Toss the cooked beets in a small bowl with just enough dressing to coat. Place the beets on the prepared baking sheet and roast until the beets are slightly caramelized, stirring occasionally, about 12 minutes. Set aside and cool. Toast the walnuts on a separate sheet pan, for 5-7 minutes, tossing once. Coarsely chop.
Toss the arugula, walnuts, and cranberries in a large bowl with enough vinaigrette to coat. Season the salad, to taste, with salt and pepper. Mound the salad onto 4 plates. Arrange the beets around the salad. Sprinkle with goat cheese, and serve.