In a medium saucepan, cook the rice according to the package directions.
Meanwhile, heat the oil in a soup pot over medium-high heat. Add the sausage and cook for 5 to 6 minutes, or until brown. (If you use raw sausage, cook for 8 to 10 minutes, or until brown and cooked through.) Remove the sausage.
In the same pot, add the mushrooms and cook for 5 to 8 minutes, or until soft and browned. Add the water, scraping up the sausage bits stuck to the bottom of the pan. Add the thyme, pepper flakes, kale, and wine. Cook for 4 minutes, or until the kale is wilted. Add the broth and simmer for 15 minutes. Season to taste with pepper.
When the rice is cooked, stir it into the soup along with the sausage. Simmer for 5 minutes, or until hot.