Start by seasoning the bone-in chicken breasts with kosher salt and freshly ground black pepper. In a large heavy-bottomed pot, heat 2 tablespoons of vegetable oil over medium-high heat. Add the chicken breasts and sear them until golden brown on both sides, about 5-7 minutes per side. Once browned, remove the chicken from the pot and set it aside.
In the same pot, add the remaining 1/2 cup of vegetable oil. Gradually whisk in 1 cup of flour to create a roux. Cook the roux over medium heat, stirring constantly, until it turns a deep brown color, similar to chocolate. This process takes about 20-30 minutes, so be patient and avoid burning it.
Once the roux is ready, add the diced onions, celery, and bell peppers to the pot. Sauté the vegetables for about 5-7 minutes until they are softened. Stir in the minced garlic and cook for an additional minute.
Sprinkle in the cayenne pepper, oregano, basil, thyme, and bay leaves. Stir well to combine. Next, pour in the chicken broth and bring the mixture to a boil. Once boiling, lower the heat to a simmer and return the seared chicken to the pot. Cover and let it simmer for about 30 minutes.
After 30 minutes, add the sliced and quartered andouille sausage to the pot. Continue to simmer for another 30 minutes, allowing all the flavors to meld together. Stir occasionally to prevent sticking.
Remove the chicken breasts from the pot and shred the meat, discarding the bones. Return the shredded chicken to the gumbo along with the filé powder or gumbo seasoning. Stir well and adjust seasonings to taste, adding more salt, pepper, or cayenne if desired. Let it simmer for an additional 10 minutes.
Serve your delicious Sausage and Chicken Gumbo over a generous scoop of cooked white rice. Enjoy with your favorite hot sauce for an extra kick!