Cook the pasta according to the package directions. Drain and keep warm.
While the pasta is cooking, combine 1 tablespoon Cajun seasoning and ½ teaspoon each of salt, pepper, and thyme. Season the shrimp and chicken evenly with this spice mixture.
Heat a small amount of olive oil in a large saute pan over medium heat. Cook the shrimp in the hot pan, cooking on each side for 2 - 3 minutes, until the shrimp turn pink and curl. Remove the shrimp from the pan immediately, and set aside on a covered plate to keep warm.
Add a little more oil to the pan and cook the seasoned chicken until cooked through, about 7 minutes. Remove the chicken and set aside on the covered plate with the shrimp.
Add the sausage to the pan. Warm the sausage and brown it slightly, then remove and keep warm on the covered plate with the chicken and shrimp.
Add the remaining oil to the pan, and cook the onion, green pepper, and garlic for 3 - 4 minutes. Stir in 1 tablespoon of Cajun seasoning, ½ teaspoon salt, crushed tomatoes, broth, and heavy cream. Bring to a simmer and cook for 2 - 3 minutes.
Remove from the heat and stir in the parmesan cheese, until the cheese is melted and the sauce is fully combined.
Add the cooked, drained pasta to the sauce, and toss to coat. Then add the shrimp, chicken, and sausage.
Serve immediately, garnished with parsley and a little extra grated parmesan if desired.
