Preheat oven to 375°F.
Season chicken cubes all over with garlic powder, paprika, salt, and pepper.
In a large, 15-inch oven-safe skillet over medium-high heat, melt the butter. Once melted, add chicken and cook for 4-5 minutes on each side, or until golden brown. The chicken will not be completely cooked through.
Transfer chicken to a plate and tent to keep warm.
Reduce the heat of the skillet to medium-low. Add onions. Cook until softened (about 3 minutes). Add garlic and cook for 1 more minute.
Sprinkle flour over the onion mixture, and whisk to combine. Pour in the chicken stock, followed by heavy cream, whisking constantly. Increase heat to medium. Simmer for 6-8 minutes or until the mixture has reduced and thickened slightly.
To the skillet, add ½ cup of mozzarella, ½ cup of Monterey jack, and ½ cup of parmesan cheese. Stir to combine.
Add uncooked noodles, broccoli, and seared chicken. Stir to combine, making sure the noodles, broccoli, and chicken are all covered with the sauce.
Top with the remaining cheeses, cover with aluminum foil, and transfer to the oven. Bake for 24-27 minutes, or until the cheese is melted, the pasta is tender, and the sauce is bubbly. The chicken is fully cooked when it reaches an internal temperature of 165°F.
Remove the foil. Cook for an additional 3-5 minutes, or until the cheese has browned.
Serve garnished with parsley.