Heat a large pot or Dutch oven over medium-high heat; add the olive oil. Add the sausages and cook, stirring occasionally, until lightly browned, about 3 minutes. Transfer to a plate using a slotted spoon.
Add the scallion whites, celery and bell pepper to the pot. Cook, stirring occasionally, until softened, about 2 minutes. Add the garlic and Cajun seasoning; cook 1 minute.
Add 1 1/2 cups water, the chicken broth, rice, tomatoes and bay leaf. Bring to a simmer and cook until the rice is tender, about 15 minutes. Return the sausages to the pot and season with salt. Discard the bay leaf. Top the soup with the scallion greens and serve with cornbread.