In a large pot or Dutch oven, heat the vegetable oil over medium heat. Gradually whisk in the flour, stirring constantly until the roux turns a deep brown color, about 20-30 minutes.

Sauté Vegetables

Add the chopped onion, green bell pepper, celery, and garlic to the roux. Cook for about 5 minutes until the vegetables are tender.

Add Meats

Slice the Andouille sausage and add it to the pot along with the chicken thighs. Brown the meats for about 5 minutes.

Simmer the Gumbo

Stir in the canned diced tomatoes, chicken broth, bay leaves, thyme, cayenne pepper, salt, and black pepper. Bring to a boil, then reduce heat and let simmer for 45 minutes, stirring occasionally.

Add Shrimp

Add the shrimp and cook for an additional 5-10 minutes until they are pink and cooked through.

Finish and Serve

Remove bay leaves before serving. Stir in the fresh parsley and serve the gumbo over cooked white rice.