In a medium saucepan, combine the broth and wild rice, cover partially and simmer, stirring occasionally, for 30 minutes.
Meanwhile, heat the oil in a large Dutch oven or pot over medium-high heat. Add the sausage and cook, stirring occasionally, until browned, about 5 minutes. Add the onion, celery and mushrooms and cook until the onions are softened, about 3 minutes.
Add the cooked wild rice and its broth to the sausage and vegetables and simmer, uncovered, until the rice is tender, about 15 minutes. Add the cream and heat through. Season to taste with salt and pepper.