Heat the vegetable oil in a large pot over medium-high heat. Cook the chicken until no longer pink in the center and the juices run clear, 3 to 5 minutes. Remove from pot and set aside.
Melt the butter in the large pot. Cook the onion, green onion, and parsley in the butter until the onions begin to soften, 4 to 7 minutes. Stir in the garlic and cook until brown, 3 to 4 minutes. Add the chicken broth, cooked chicken, sausage, and rice; bring to a boil for 2 minutes and then reduce heat to medium-low. Cover and simmer for 1 hour. Do not remove cover or stir while simmering. Serve hot.
