Wash beets and greens well. Cut off all but 1/4" of the tops, discard large stems, and set leafy greens aside.
Preheat oven to 375° F. Place beet bottoms (the roots with the bit of stem attached) in a roasting pan, toss with olive oil and add rosemary sprigs. Roast for about 40 minutes if they are baby beets, longer if they are big beets. Cook until just tender (can be pierced with a fork). Allow to cool slightly. Remove skin while warm, and cut beets in half.
Meanwhile sauté the beet greens in olive oil and add a splash of balsamic vinegar. Season the greens with salt and pepper and place on plate. Top with roasted beets and serve.