In a large pot, heat 1 tablespoon of olive oil over medium heat. Add diced boneless skinless chicken thighs and sliced andouille sausage. Cook for about 6-8 minutes until browned and charred. Remove meat and set aside.

Lower the heat and add another tablespoon of olive oil along with 2 tablespoons of unsalted butter. Once melted, whisk in 1/4 cup of flour to create a roux. Stir constantly for about 10 minutes until deep golden brown.

Add diced onion, chopped green bell pepper, and diced celery to the roux. Sauté for 5 minutes until softened. Add minced garlic and cook for another minute.

Mix in 2 tablespoons of tomato paste and deglaze with 1/2 cup of chicken broth. Pour in the remaining broth, with 2 tablespoons of Cajun seasoning and 1 teaspoon of salt.

Reintroduce chicken and sausage to the pot. Simmer gently, then reduce heat to low. Cover and let it simmer for 15-20 minutes, stirring occasionally.

Serve over steamed white rice and adjust heat with hot sauce to taste.