In a Dutch oven or large pot over medium heat, cook the sausage until browned and the fat is rendered, about 5 minutes. Drain on paper towels and set aside.
To the fat in the pan, add the oil and heat over medium-high heat. Add the onions, celery, bell peppers, bay leaf, salt, and cayenne and cook, stirring, until the vegetables are soft, about 4 minutes. Add the garlic and cook, stirring, until fragrant, 30 seconds. Add the red beans and their juices, cooked sausage, and 3 cups of the chicken stock, stir well to mix, and bring to a boil. Reduce the heat and simmer uncovered, stirring occasionally, until thick and reduced slightly, about 30 minutes, adding more stock as needed if the mixture gets too thick.
Remove from the heat and discard the bay leaf. (If desired, the soup can be pureed at this point using a hand-held immersion blender, or in batches in a food processor.)
To serve, ladle the soup into bowls and top each portion with 1 to 2 tablespoons of the cooked rice. Garish each serving with scallions and serve immediately.