Cook penne until al dente, according to package directions. Remove pasta from the pot with a slotted spoon and reserve cooking water. Once cooked, drizzle pasta with a little olive oil to prevent it from sticking and save.
Return pasta water to a boil, and add broccoli florets. Cook just until tender but not mushy, about two minutes. Drain and plunge florets into ice water to stop the cooking process and help them retain their bright green color
Coat the chicken with cajun seasoning and heat oil in a large skillet. Saute chicken, turning once until fully cooked. Transfer to a plate and reserve. Preheat oven to 350F.
To make sauce: wipe the skillet used to cook the chicken with a paper towel, return to the stove and melt butter over medium heat until bubbly. Add garlic and cook for 30 seconds.
Pour wine into skillet and simmer until reduced by half. Whisk in cream and simmer until thickened, about two minutes. Add Parmesan cheese and mix until melted.
Mix sauce into reserved pasta until well combined
Pour pasta into a 9 x 13 inch baking dish and top with chicken and broccoli florets. Top with Parmesan cheese and bake for 20 mins until heated through