Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Add the chicken pieces and cook, stirring occasionally, until browned on all sides, about 5-6 minutes. Remove the chicken from the pot and set aside.
Add the sliced smoked turkey sausage to the pot and cook until browned, about 3-4 minutes. Remove and set aside with the chicken.
Reduce heat to medium. Add the diced onion, green bell pepper, red bell pepper, and celery to the pot. Cook, stirring occasionally, until vegetables are softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the diced tomatoes with their juices, chicken broth, tomato paste, Cajun seasoning, smoked paprika, dried thyme, dried oregano, and cayenne pepper. Stir well to combine.
Return the browned chicken and sausage to the pot. Bring the mixture to a boil.
Add the penne pasta to the pot, stirring to submerge the pasta in the liquid.
Reduce heat to medium-low, cover, and simmer for 15-18 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Season with salt and freshly ground black pepper to taste.
Remove from heat and let stand, covered, for 5 minutes to thicken.
Serve garnished with sliced green onions and chopped fresh parsley.