Put oven rack in middle position and preheat oven to 425°F.

Place beets on a piece of foil. Drizzle with olive oil and season with salt and pepper. Bake for 1 hour until tender. Allow to cool in foil for 30 minutes.

When beets are cool enough to handle, peel them, discarding stems and root ends, then cut into 1/2-inch cubes.

While beets are cooling, bring broth and water to a bare simmer in a 2- to 3-quart saucepan. Keep at a bare simmer, covered.

Cook onion in oil in a wide 4- to 6-quart heavy pot over moderate heat, stirring occasionally, until softened, about 3 minutes. Add rice and cook, stirring constantly, 1 minute.

Add wine and simmer briskly, stirring constantly, until absorbed, about 1 minute. Stir in 1/2 cup broth and simmer briskly, stirring constantly, until broth is absorbed. Continue simmering and adding broth, about 1/2 cup at a time, stirring constantly and letting each addition be absorbed before adding the next, until rice is just tender and creamy-looking, 18 to 22 minutes. (Reserve leftover broth.)

Stir in beets, salt, and pepper and cook, stirring, until heated through. Thin as necessary with some of leftover broth, then stir in cheese and remove from heat.