Line a baking sheet with foil. Preheat oven to 450°F.
Whisk vinegar, shallots and honey in a medium bowl to blend. Gradually whisk in the oil. Season the vinaigrette, to taste, with salt and pepper.
Toss the beets in a small bowl with 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.
SALAD
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 atop 4 plates. Arrange the beets around the salad. Sprinkle with the avocado and goat cheese, and serve.
Notes
You can also use dried cherries in place of cranberries.
Look for cooked beets in the produce section at Trader Joes or at well-stocked grocery stores. To cook them yourself, roast them in the oven until a knife can slip through the beet easily.