Melt 2 tablespoons butter and vegetable oil in large skillet or Dutch oven over medium high heat. Add cubed chicken breast and andouille sausage slices, cook for 5-6 minutes, stirring occasionally so all sides are lightly browned, and the chicken is cooked through. Using a slotted spoon, remove from pan and set aside. Use a spoon to scrap all the bits off the bottom and leave in the pan for the next step.
Lower heat to medium, add the additional 2 tablespoons of butter and sauté the celery, onion, bell pepper and garlic. for 7-8 minutes or until vegetables soften.
In a medium bowl, combine shrimp with salt, black pepper, smoked paprika, cayenne pepper, and parsley.
Add crushed tomatoes, chicken stock, creole seasoning, thyme, bay leaves and hot sauce. Cook for 5 minutes then add rice and cook for about 15 minutes until the rice is tender, stirring every 5 minutes so the rice does not stick to the bottom. Add more broth if the rice is too al dente.
Before the rice is thoroughly cooked, add shrimp and stir occasionally until they are cooked through, pink. Add chicken and sausage back to pan and cook until they are warmed through, Season with kosher salt to taste. Serve garnish with green onions. Bon Appetit!