Cook onions in 2 tablespoons hot oil in a Dutch oven over medium heat, stirring occasionally, 30 to 35 minutes or until caramelized. Remove from pan, and set aside.
Heat remaining 1 tablespoon oil in Dutch oven; add garlic, and sauté 2 minutes. Add rice; cook, stirring constantly, 2 minutes.
Reduce heat to medium; add 1 cup chicken broth. Cook, stirring often, until liquid is absorbed. Repeat procedure with remaining chicken broth, 1 cup at a time. (This takes about 30 minutes.) Stir in onions.
Add wine; cook, stirring gently, until liquid is absorbed. Stir in cheese, butter, and salt. Serve immediately.