Bring a large pot of salted water to a boil and cook the pasta to al dente. Reserve 1/4 cup of the pasta liquid.
Melt 1 tablespoon butter over medium-high heat in a large skillet. Season shrimp with salt and pepper and add shrimp to skillet. Sauté 2-3 minutes. Remove shrimp and set aside.
Add 1 tablespoon olive oil to skillet. Season chicken with salt and pepper and add to skillet. Cook until no longer pink in the middle, stirring once or twice, about 3 to 4 minutes. Remove from skillet and place with shrimp.
Add 1 tablespoon butter and Andouille sausage, onion, green pepper, red pepper, and celery. Cook 4 to 5 minutes, until Andouille is browned and vegetables are softened.
Add garlic, paprika, garlic powder, oregano, and thyme and cook 30 seconds. Then add Worcestershire sauce, diced tomatoes, tomato paste, and chicken broth. Let simmer 3 minutes.
Add cream and simmer 3 minutes. Return shrimp and chicken and add cooked pasta plus reserved cooking liquid. Simmer another 2-3 minutes. Check for seasoning and add salt to taste.
To serve, top with green onions.