Preheat oven to 275 degrees. Bring chicken broth to a boil in a medium saucepan. Stir in rice, 2 tsp. Cajun seasoning, and garlic. Lower to a simmer and let cook for 15 min., covered. Turn off heat and let stand for 5 min.
Heat 1 Tbsp. vegetable oil in a 12-inch or larger cast iron pan over medium-high heat. Add Andouille sausage and brown on both sides, 2 to 3 min. per side. Using a slotted spoon, remove sausage, dice, and set aside. To the pan, add onion, peppers, and celery. Season with salt and pepper and saute for 3 to 4 min. Let your cast iron pan cool and wipe clean with a paper towel.
In a 12-inch or larger non-stick pan, heat 2 Tbsp. butter and remaining 2 Tbsp. vegetable oil over medium-high heat. Add cooked rice evenly into the pan and let cook undisturbed for 5 to 7 min. Use a spatula to gently push in and lift up rice to check for desired crispiness. The rice should be a light brown color. Toss and repeat for another 5 to 7 min. Stir in browned sausage and vegetables and again press rice evenly into the pan and heat for another 6 to 7 min. Total process should take about 18 to 20 min.
Heat the cast iron pan over high heat. Melt the remaining 4 Tbsp. butter in the microwave. Toss chicken in melted butter and liberally season with salt and pepper and remaining Cajun seasoning. When cast iron pan is smoking, place chicken in pan so that the pieces are not touching (cook in batches if needed). Cook for 1 1/2 to 2 min on each side or until both sides are blackened. After all pieces are blackened, place all chicken in the cast iron pan and put on the middle rack in the preheated oven. Cook for 8 to 10 min. or until chicken reaches 165 degrees internally. Remove and set aside to rest for 5 min. Slice chicken across the grain into 1/2-inch strips and fold into crispy rice. Serve hot with your favorite hot sauce.