Trim beans, and cut into bite-size pieces. Bring beans and 1/4 cup broth to a boil in a Dutch oven over medium-high heat; cook 10 minutes or until crisp-tender. Remove beans with a slotted spoon, and set aside.
Bring remaining broth to a simmer in a saucepan (do not boil), keeping warm over low heat.
Add butter, chopped onion, and garlic to broth in Dutch oven; cook 3 minutes. Add rice and white wine, and cook, stirring constantly, 5 minutes or until liquid is absorbed. Reduce heat to medium.
Add 1 cup simmering broth to rice mixture in Dutch oven, and cook, stirring often, until liquid is absorbed. Repeat procedure with remaining broth, 1 cup at a time. (Cooking time is about 15 to 20 minutes.)
Stir in beans, thyme, pepper, and Parmesan cheese; serve immediately.
Asparagus Risotto: Substitute 1 pound fresh asparagus for green beans. Proceed as directed.