Bring the broth to a simmer in a saucepan over medium-high heat; cover and keep warm.
Meanwhile, heat the olive oil in a large saucepan over medium heat. Add the onion and cook until soft, about 4 minutes. Add the rice and cook, stirring, 1 minute. Reduce the heat to medium low. Stir in the wine until the liquid is absorbed, about 3 minutes.
Ladle in 3/4 cup hot broth and cook, stirring constantly, until the liquid is absorbed, 6 to 7 minutes. Repeat with the remaining broth, adding 3/4 cup at a time, until the rice is tender but somewhat chewy, about 50 minutes.
Stir in 3/4 teaspoon salt, pepper to taste and 1/2 cup parmesan. Divide among bowls. Top with the remaining 1/4 cup parmesan and the basil.