Preheat the oven to 350°F (175°C).
In a large pot of salted boiling water, cook the pasta shells according to package instructions until al dente. During the last 2-3 minutes of cooking, add the broccoli florets. Drain the pasta and broccoli in a colander and set aside.
In a large skillet over medium heat, combine the cooked chicken, garlic powder, onion powder, salt, and pepper. Stir for about 2 minutes until heated through.
In a mixing bowl, combine 1 ½ cups of cheddar cheese, cottage cheese, milk, and the chicken mixture. Mix well until combined.
Add the drained pasta and broccoli to the skillet, stirring gently to combine all ingredients.
Transfer the mixture to a 9x13 inch baking dish.
Top with the remaining cheddar cheese and the grated Parmesan cheese.
Bake in the preheated oven for 20-25 minutes or until the cheese is bubbly and golden brown on top.
Remove from the oven and let it cool for 5 minutes before serving.