Bring a large pot of salted water to a boil. Cook penne until al dente according to package directions. Reserve 1/2 cup pasta water, then drain.
Toss chicken strips with 1 tablespoon of the Cajun seasoning. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Cook chicken until golden and internal temperature reaches 165°F (74°C), about 5-6 minutes, turning once. Transfer to a plate.
In the same skillet, add remaining 1 tablespoon olive oil. Sauté bell pepper and onion until softened, about 4 minutes. Add garlic and remaining 1 tablespoon Cajun seasoning; cook 1 minute until fragrant.
Pour in chicken broth, scraping up any browned bits. Stir in heavy cream and bring to a gentle simmer. Whisk in Parmesan cheese until smooth. Season with salt and black pepper to taste.
Add the drained pasta and cooked chicken back to the skillet. Toss well to coat everything in the sauce. Add a little pasta water if needed for a silky consistency. Serve immediately, garnished with parsley.