Mix together the chicken spice rub ingredients together in a shallow bowl. Remove the chicken from it's package and spread the rub all over the chicken on all sides. Heat an outdoor grill to medium-high heat. Place the chicken onto the grill and let cook on both sides until no longer pink in the center. While the chicken is cooking, begin making the alfredo sauce.
Boil a pound of noodles (any shape will do) in a large pot of water. Boil until the pasta is al dente, drain and set aside.
For the sauce, dice the onion into small pieces. In a saute pan place the half stick of butter and the onions and let them come to high heat and begin to soften. Once the onions are softened, add the cornstarch and continue to mix. Add the seasonings to the onions. Add the whipping cream to the sauce and turn the heat down to medium heat and saute until it begins to simmer and thicken. Add the parmesan cheese and get ready to serve. You can add roasted broccoli to the pasta if you desire.
Take the cooked chicken from the grill and slice into thin slices. Drain the cooked pasta and place the pasta on a plate. Add the broccoli alfredo sauce on top of the pasta and top with the seasoned and sliced chicken. Serve with extra parmesan cheese if you .