Melt butter in a saucepan over medium heat. Stir in flour and cook for 1 minute. Gradually whisk in milk and cook until slightly thickened, 3–5 minutes.
Add 1 cup cheddar, garlic powder, onion powder, paprika (if using), salt, and pepper. Stir until smooth. Set aside.
Mix diced chicken, chopped broccoli, ½ cup cheddar, and ricotta (if using) in a large bowl until well combined.
Fill each cooked shell with the chicken-broccoli mixture. Avoid overstuffing to prevent tearing.
Grease a 9x13-inch baking dish. Arrange shells open-side up. Pour cheese sauce over them evenly. Cover with foil and bake at 350°F (175°C) for 20 minutes, then uncover and bake 5 more minutes.
Cool slightly before serving. Garnish with extra cheese or fresh parsley if desired.