01 - Cook pasta according to package directions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
02 - Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add sausage slices and cook until browned, about 3-4 minutes. Remove and set aside.
03 - Season chicken pieces with half the salt and pepper. Add to skillet and cook until just cooked through, about 5-6 minutes. Remove and set aside with the sausage.
04 - Add remaining olive oil to the skillet. Sauté onion, bell peppers, and celery until softened, about 5 minutes. Stir in garlic and cook for 1 minute more.
05 - Return sausage and chicken to skillet. Add shrimp, paprika, oregano, thyme, cayenne, and remaining salt and pepper. Cook, stirring, until shrimp are pink and opaque, about 3 minutes.
06 - Pour in chicken broth and bring to a simmer. Reduce heat, stir in heavy cream, and cook for 2-3 minutes until slightly thickened.
07 - Add drained pasta and Parmesan cheese. Toss everything together, adding reserved pasta water as needed for a creamy sauce. Remove from heat, sprinkle with parsley and green onions, and serve hot.