Put oven rack in middle position and preheat oven to 425 ° F.
Tightly wrap beets on foil and roast on baking sheet until tender, about 1 1/2 hours. Remove and let them cool slightly. Peel the beets under running cold water. Place two of the beets in a blender or food processor and process briefly, until slightly smooth. Dice the remaining beet into small cubes.
While the beets are cooling, bring the broth and water to a simmer in a pan.
Heat butter in a large, heavy pot over moderate heat. Cook the garlic and onion until softened and fragrant. Add the rice and cook, stirring constantly, for 1 minute.
Add wine and stir until absorbed, about 1 minute. Using a ladle, stir in 1/2 cup warm broth and simmer briskly, stirring constantly, until broth is absorbed. Continue simmering and adding warm broth, one ladle at a time, stirring constantly and letting each addition be absorbed before adding the next, until rice is just tender and creamy-looking, for about 18 to 22 minutes.
Stir in the beets, vinegar, salt, and pepper and cook, stirring, until heated through.
Serve immediately the risotto, adding some crumbled goat cheese or parmesan flakes.