Preheat oven to 375°F (190°C). Grease a baking dish (about 9x13 inches) with olive oil.
Cook the pasta according to package instructions until al dente. Drain and set aside.
Steam or blanch the broccoli florets in boiling water for about 3 minutes until bright green and just tender, then drain and set aside.
In a large mixing bowl, examine the cream cheese. Use a hand mixer to blend in the chicken broth, garlic powder, onion powder, salt, and pepper until smooth.
Mix in the shredded chicken, cooked pasta, and steamed broccoli until combined.
Add half of the mozzarella and Parmesan cheeses into the mixture, mixing until well incorporated.
Transfer the chicken, broccoli, and pasta mixture into the prepared baking dish. Spread evenly.
Top with the remaining mozzarella and Parmesan cheese, then sprinkle with red pepper flakes if using.
Bake in the preheated oven for 25-30 minutes or until the cheese is bubbling and slightly golden.
Remove from oven and let it cool for a few minutes before serving.
Notes
Serve hot out of the oven, garnished with freshly chopped parsley or basil.