Bring a large pot of salted water to a boil, add the penne and cook about 9 minutes until al dente.
During the last 2–4 minutes of the pasta cooking time, add the frozen broccoli to the pot and cook until tender; drain pasta and broccoli in a colander.
In a small bowl, combine paprika, salt, garlic powder, black pepper, onion powder, cayenne, oregano, and thyme.
Toss the cubed chicken with 2–3 tablespoons Cajun seasoning until evenly coated.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook, stirring occasionally, until cooked through and no longer pink, about 6–8 minutes; transfer chicken to a plate and keep warm.
Reduce heat to medium-low and add butter to the same skillet. Stir in minced garlic and cook 30 seconds until fragrant.
Whisk in the chicken broth, heavy cream, and flour. Cook over medium-low, whisking frequently, until the sauce thickens and starts to bubble, about 3–5 minutes.
Return the cooked chicken to the skillet, then add the drained pasta and broccoli. Toss gently to coat everything in the sauce and heat through.
Remove from heat, sprinkle with the shredded Parmesan, toss briefly, and serve immediately.