Bring a large pot of salted water to a boil. Add the pasta shells and cook according to package instructions until al dente. In the last 3 minutes of cooking, add the broccoli florets. Drain and set aside.

In a skillet over medium heat, melt the butter. Stir in the flour and cook for 1-2 minutes until golden. Gradually whisk in the milk, stirring constantly until the mixture thickens.

Reduce heat to low, then add the cheddar cheese, cream cheese, garlic powder, onion powder, salt, and pepper. Stir until the cheese is melted and the sauce is smooth.

In a large mixing bowl, combine the cooked pasta, broccoli, chicken, and cheese sauce. Mix well to coat everything evenly.

Transfer the mixture to an oven-safe baking dish. If desired, sprinkle bread crumbs and parmesan cheese on top.

Preheat the oven to 350°F (175°C) and bake for 20 minutes until bubbly and golden on top.