Cook the pasta to al dente. When done, remove the pasta, but save the pasta water.
Roast the broccoli: drizzle olive oil, salt, pepper over broccoli. Seperate evenly onto large baking sheet lined with parchment paper. Roast in the oven for 25 minutes.
Meanwhile, cut the chicken breasts across to make 4 thinner chicken breasts.
Mix all chicken seasoning ingredients well, then sprinkle evenly over both sides of chicken breasts.
Shread the mozzarella, set aside.
Set a large skillet to medium/medium-high heat. Place chicken onto pan and let cook for 5 minutes. Flip, cook another 5 minutes.
Remove chicken from pan and remove pan from heat, but do not clean. Slice the chicken into bite sized cubes while the pan cools slightly (NOTE: You don’t want the pan to cool completely, just to a simmer level, so that the garlic does not burn)
Set the pan back on to medium-low heat, and add the white wine and minced garlic. Swirl to deglaze, about 30 seconds.
Add the butter, heavy cream, mozzarella. Continuously stir till all combined. Spoon in pasta water as needed if the sauce is too thick.