Fill a large stock pot with water and bring to a rolling boil.
Add the penne pasta and cook according to package directions, about 9 minutes.
During the last 2–4 minutes of pasta cooking, add the frozen broccoli to the pot and continue boiling until broccoli is tender.
Drain the pasta and broccoli in a colander and set aside.
While pasta is cooking, season the cubed chicken with 2 teaspoons paprika, 1 teaspoon salt, 1 teaspoon garlic powder, 1 teaspoon black pepper, 1 teaspoon onion powder, 1 teaspoon cayenne, 1 teaspoon oregano, and 1 teaspoon thyme (or use 2–3 tablespoons prepared Cajun seasoning), mixing to coat.
Heat 2 tablespoons oil in a large skillet over medium-high heat and cook the seasoned chicken until cooked through and no longer pink, about 5–7 minutes. Remove chicken and keep warm.
In the same skillet, melt 2 tablespoons butter over medium-low heat, then add 1 tablespoon minced garlic and cook briefly until fragrant.
Whisk in 1/2 cup chicken broth, 1 cup heavy cream, and 2 tablespoons flour; cook over medium-low, whisking, until the sauce begins to thicken and bubble.
Add the cooked chicken, drained broccoli, and drained pasta to the skillet and toss to coat in the sauce.
Sprinkle 1/2 cup shredded Parmesan cheese over the pasta, stir until combined, then serve hot.