Prepare the chicken:Cook chicken breasts in a slow cooker with a little broth, salt, and pepper for 3 hours on high or 6 hours on low. Shred once cooked.Shortcut: You may also use rotisserie chicken to save time.
Prepare the broccoli:Steam fresh broccoli or microwave steam-in-bag broccoli according to package directions. Drain well.
Preheat oven:Preheat oven to 375°F and lightly grease a 9×13-inch casserole dish.
Make the cheese sauce:In a saucepan over low–medium heat, melt butter with heavy cream, garlic powder, and ½ teaspoon Italian seasoning. Whisk in softened cream cheese until smooth.
Add cheeses:Stir in shredded cheddar, mozzarella, and Parmesan, reserving ¼ cup cheddar and ⅛ cup of the other cheeses for topping. Stir until fully melted and smooth.
Assemble:Layer shredded chicken in the casserole dish, followed by broccoli. Pour cheese sauce evenly over the top.
Top and bake:Sprinkle reserved cheese over the casserole, then add paprika, parsley, and remaining Italian seasoning.
Bake:Bake uncovered for 30 minutes, until hot and bubbly.
Serve:Let rest a few minutes before serving.