Preheat oven to 375°F. Spray 9×13 baking dish with non-stick cooking spray.
Bring a large pot of salted water to a boil and add pasta. Cook according to package until pasta is al dente (no more than 6 minutes total). In the last 2 minutes, stir in broccoli florets. Strain pasta and broccoli, run under cold water to stop cooking, and set to the side.
In a mixing bowl, toss chicken pieces with paprika, garlic powder, onion powder, and salt and pepper.
Heat a large saute pan with olive oil to medium-high. Add seasoned chicken pieces and cook for 4 - 5 minutes total, until no longer pink on the outside.
Add fresh spinach, mix, and cook for 1 - 2 minutes until wilted.
Remove from heat and add pasta sauce, chicken broth, and stir.
Add the cooked pasta, broccoli, parmesan cheese, and ½ cup mozzarella cheese. Gently stir to combine, then pour into prepared baking dish.
Top with the leftover mozzarella cheese and extra parmesan.
Bake for 10 - 14 minutes. Then broil for 2 - 4 minutes until the cheese is melted, bubbly, and slightly browned.