In a large pot bring water to a boil and add 8 ounces pasta shells. Cook according to package directions.
Add 12 ounces broccoli florets to the boiling water for the last 3 minutes of cooking. Drain and set aside.
Add 2 tablespoons unsalted butter in the same pot and melt over medium heat. Whisk in ¼ cup all-purpose flour and cook for 1 minute to create a roux. Slowly whisk in 2 cups milk, 2 cups shredded sharp cheddar cheese, ½ teaspoon onion powder, and ½ teaspoon garlic powder. Bring the sauce to a boil over medium-high heat until it starts to thicken.
Add the pasta shells, broccoli, and 1 pound cooked boneless skinless chicken breast, and toss to coat in the sauce. Season with salt and pepper to taste then serve immediately.