Bring a large pot of salted water to a boil. Add your pasta and cook according to package directions until al dente. Reserve about 1 cup of pasta water before draining.

Pat the shrimp and chicken dry. Season with a pinch of salt, pepper, and a dash of paprika. In a large skillet or Dutch oven, heat 1 tablespoon olive oil over medium-high heat. Add the andouille sausage and cook until browned, about 3 minutes per side. Remove to a plate. Add another tablespoon oil, then sear the chicken pieces until golden, about 4 minutes. Remove to the same plate. Finally, sear the shrimp for 2 minutes per side, just until pink. Set aside with the other meats.

Reduce heat to medium. Add a splash of olive oil if needed. Cook the onion, bell pepper, and celery (the Holy Trinity) until soft and translucent, about 5 minutes. Stir in the garlic and cook for 30 seconds more.

Sprinkle the flour over the vegetables and stir constantly for 2 minutes. This blonde roux will thicken the sauce and give it a nutty undertone. Keep stirring; you do not want it to burn.

Slowly pour in the chicken broth while whisking to remove lumps. Add the white wine if using. Bring to a simmer, then add the heavy cream, paprika, cayenne, thyme, oregano, and bay leaf. Let it bubble gently for 5 minutes, stirring occasionally.

Return the cooked sausage, chicken, and shrimp to the skillet. Stir to coat in the sauce. Add the drained pasta and toss gently. If the sauce seems too thick, add a splash of the reserved pasta water until it reaches your desired consistency. Taste and adjust salt and pepper.

Remove the bay leaf. Sprinkle with fresh parsley and Parmesan if using. Serve immediately in big bowls.