In a large saucepan or dutch oven saute' onion, carrot, green pepper, celery, garlic and chopped mushrooms in butter until tender. Stir in flour until blended. Gradually add broth, whisk together until blended. Stir in rice, sausage, salt and pepper. Bring to a boil over medium heat, stir constantly for for 2 minutes. Stir in milk and hot sauce.