In a medium saucepot, heat broth to boiling. Cover, and reduce the heat to low, holding at a simmer.
In a wide, deep skillet, heat oil over medium heat. Add onion, and sauté until translucent—about 4 minutes. Add garlic, and cook 1 minute. Stir in rice and beets; cook for 2 minutes. Add wine, 1 cup of broth, and salt; simmer until liquid is completely absorbed.
Begin adding 3 cups of the hot broth in 1-cup increments, stirring constantly until each addition is absorbed before adding the next one. (This should take 15 to 18 minutes total.) Add the remaining broth in ½-cup increments, stirring constantly. Test the risotto between additions until it’s done cooking.
Add both cheeses and basil, stirring until well combined. Divide among four plates, and serve promptly.