01 - Cook pasta according to package directions until al dente. Drain thoroughly, reserving 1/2 cup pasta water, and set aside.
02 - Toss shrimp with 1 teaspoon Cajun seasoning. Season chicken pieces generously with salt, pepper, and remaining 1 teaspoon Cajun seasoning.
03 - Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add seasoned chicken and sliced sausage; cook 4 to 5 minutes until well-browned and cooked through. Transfer to a plate.
04 - Add remaining olive oil and butter to the skillet. Place shrimp in pan and cook 1 to 2 minutes per side until just opaque and pink. Remove and set aside with chicken.
05 - In the same skillet, cook diced onion and sliced peppers for 3 to 4 minutes until softened. Add minced garlic and cook 1 minute until fragrant.
06 - Stir in diced tomatoes, tomato paste, Cajun seasoning, smoked paprika, cayenne, and thyme. Cook mixture for 2 minutes to develop flavors.
07 - Pour in chicken broth and heavy cream, scraping up browned bits from bottom of pan. Simmer for 3 to 4 minutes until slightly thickened.
08 - Return cooked chicken, sausage, and shrimp to the pan. Add cooked pasta and toss thoroughly to coat. Add reserved pasta water as needed to achieve desired sauce consistency. Adjust seasoning to taste and serve hot, garnished with green onions, fresh parsley, and grated Parmesan.