In a large pot, bring salted water to a boil. Add the cheese tortellini and cook according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add minced garlic and onion powder, cooking until fragrant (about 1 minute).
Stir in the shredded chicken and blanched broccoli florets. Cook for another 2-3 minutes until heated through.
Lower the heat and pour in the heavy cream, stirring to combine. Gradually add the shredded mozzarella cheese and Parmesan cheese, mixing continuously until melted and creamy.
Add the cooked tortellini to the skillet, tossing to coat the pasta in the cheesy sauce. Season with salt and pepper to taste.
Remove from heat and garnish with fresh chopped parsley.