Preheat your oven to 400 degrees F. Line a baking sheet with foil and spray with a nonstick olive oil spray. Add the chicken breasts to the pan and spray the chicken with a nonstick olive oil spray (canola oil spray may be substituted). Season the chicken with salt, black pepper, and cajun seasoning. Place it in the oven and bake for 30-35 minutes or until cooked through. Allow the chicken to rest for 5 minutes before slicing.
While the chicken is baking, prepare your pasta and squash. Bring a large pot of salted water to a rolling boil. Add the pasta and boil until al dente, about 8 minutes. Drain and transfer to a large bowl.
While the pasta is boiling, prepare your alfredo sauce. In a medium saucepan, melt 1/2 cup of the butter. Whisk in the flour and allow it to bubble and turn a golden brown for about 2 minutes. Whisk in the heavy cream and bring to a gentle simmer. Continue whisking until slightly thickened. If you find that the sauce is too thick to your liking, add more heavy cream or milk until it reaches the consistency you desire. Remove from heat and stir in the parmesan cheese until melted. Season to taste with salt and black pepper. Pour the sauce over the pasta and toss. Also add the chicken and toss. Cover the pasta and allow it to sit for 5-10 minutes. This will allow the pasta to soak up some of the sauce, and it will also allow the sauce to thicken.
While the pasta is sitting, prepare your squash. Whisk together the brown sugar, chili powder, smoked paprika, garlic powder, onion powder, salt and black pepper. Set aside.
Melt the remaining 2 tablespoons of butter in a large nonstick pan over medium heat. Add the olive oil also to the pan. Add the squash and toss to coat in the butter mixture. Season the squash with the seasoning you created in the last step. Cook the squash for about 5 minutes on each side, or until brown and caramelized.
Add the squash to the pasta and toss. Top with grated parmesan cheese and chopped parsley. Enjoy immediately!