Heat oil and butter in a dutch oven over medium high heat
Chop chicken into bite sized pieces and add to heated pan and allow to brown on once side for about 2-3 minutes
Finely chop carrots, celery, onion and garlic and add to pan and saute until tender while you continue to let chicken cook as well, about 3-4 more minutes
Stir in flour and cajun seasoning and let cook for 1-2 minutes
Very slowly pour in broth while stirring to prevent any lumps
Add shrimp and bring to a simmer for about 10 more minutes or until shrimp and chicken and fully cooked through
While soup is simmering, follow package instructions to make instant brown rice
Serve gumbo with a scoop of rice and garnished with fresh herbs, if desired