In a large, non-stick skillet, heat the olive oil over medium heat. Add the onions, cabbage and thyme and saute until the onions are golden, 10 to 12 minutes, stirring frequently.
Meanwhile, in a saucepan, combine the broth and wine and heat to simmering.
When the onions are golden, add the rice and toss to coat with oil. Add 1 cup of the simmering broth to the rice and stir until most of the liquid has been absorbed. Continue adding more broth, 1 cup at a time, cooking and stirring as the liquid is absorbed. It will take a total of 18 to 35 minutes for most of the liquid to be absorbed and the rice to become tender and creamy.
Stir in the Parmesan. Season to taste with salt and pepper if needed. Serve hot.