Place a Lodge Cast-Iron Combo Cooker on the grill. Add the sausage and cook through.
Add the olive oil, mushrooms, garlic and green onions. Cook until softened, about 5 minutes.
Add the green beans, chicken broth and soy sauce. Reduce the heat to low. Cover the skillet, and close the grill. Cook for 30 minutes, or until the beans are tender.
In a small bowl, combine the butter and flour with a fork and set aside.
Add the cream, salt and pepper to the beans. Increase the heat to medium-high. Cook uncovered for 1-2 minutes. Stir in the butter mixture. Continue cooking for about 5 minutes or until the sauce reaches your desired consistency.