Preheat oven to 400°.
Wrap each beet in aluminum foil. Bake at 400° for 1 hour and 30 minutes or until tender. Discard foil; cool beets for 30 minutes. Trim off beet roots; rub off skins. Cut beets into 1/8-inch-thick slices.
Combine cranberry juice, cranberries, sugar, and vinegar in a small saucepan. Bring to a boil; cook 11 minutes or until mixture thickens. Remove from heat. Stir in shallots, salt, and pepper. Gradually add oil, stirring with a whisk.
Combine lettuce and spinach in a large bowl. Add cranberry mixture; toss to coat. Add beets; toss gently to combine. Divide salad evenly among 6 plates. Top each salad with 4 teaspoons cheese.