Heat olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the chicken pieces to the pot and season with salt and black pepper. Cook until browned on all sides, about 5 minutes. Remove the chicken and set aside.
In the same pot, add the sliced smoked turkey sausage and cook until browned, about 3 minutes. Remove and set aside with the chicken.
Add the diced onion, green bell pepper, red bell pepper, and celery to the pot. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the diced tomatoes with their juice, chicken broth, tomato paste, Cajun seasoning, smoked paprika, and cayenne pepper. Stir well to combine.
Return the browned chicken and sausage to the pot and bring the mixture to a boil.
Add the penne pasta to the pot, stirring to submerge it in the liquid.
Reduce the heat to medium-low, cover the pot, and simmer for 15 minutes, stirring occasionally, until the pasta is cooked and most of the liquid is absorbed.
Remove the lid and cook uncovered for an additional 3-5 minutes if needed to thicken the sauce.
Taste and adjust seasoning with salt and black pepper as desired.
Remove from heat and let the jambalaya rest for 5 minutes before serving.
Garnish with sliced green onions and chopped fresh parsley.