Cook brown rice according to package instructions. Set aside.
Heat a large saute pan to medium heat. Add olive oil. When oil becomes hot, add onions, carrots and garlic. Saute until vegetables are soft. Add cooked brown rice. Cook for 2 to 3 minutes. Pour in 1/2 cup white wine, stirring continuously. Once the liquid is absorbed by the rice, add 1/2 cup chicken stock. Continue to stir. Continue this process until all the liquid has been used and absorbed. (Once all the wine has been added, continue with chicken stock. Be careful not to turn on high heat, or you will create more evaporation than absorption.) Add the mushrooms, tomatoes, thyme and cheese. Stir until cheese is well-incorporated. Add half-and-half, salt and pepper. Serve immediately.