Heat oil in large saucepan over medium heat. Add onion, 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook until soft, 4 to 5 minutes. Add sweet potatoes and garlic. Cook for 2 minutes, stirring occasionally.
Add rice and cook for 2 minutes. Add champagne and cook until absorbed, stirring frequently. Measure 3 1/2 cups water, adding 3/4 cup at a time to rice mixture. Cook, stirring occasionally, until absorbed before adding next measurement of water. After 30 minutes, all water should be absorbed.
Stir in Parmesan cheese and serve immediately.