01 - Cook pasta according to package directions until al dente. Drain and reserve 1/2 cup pasta water before setting aside.
02 - Coat shrimp with 1 tsp Cajun seasoning. Season chicken pieces with salt, pepper, and remaining 1 tsp Cajun seasoning.
03 - Heat 1 tbsp olive oil in large skillet over medium-high heat. Add chicken and sausage; cook 4 to 5 minutes until browned and cooked through. Transfer to plate.
04 - Add remaining olive oil and butter to skillet. Cook shrimp 1 to 2 minutes per side until just opaque. Remove and set aside.
05 - In same skillet, cook onion and peppers 3 to 4 minutes until softened. Add garlic and cook 1 minute until fragrant.
06 - Stir in tomatoes, tomato paste, Cajun seasoning, smoked paprika, cayenne, and thyme. Cook 2 minutes to meld flavors.
07 - Pour in chicken broth and heavy cream, scraping browned bits from bottom. Simmer 3 to 4 minutes until slightly thickened.
08 - Return chicken, sausage, and shrimp to pan. Add pasta and toss to coat, adding pasta water as needed for consistency. Adjust seasoning. Serve hot garnished with green onions, parsley, and Parmesan if desired.