Preheat the oven to 375°F (190°C) and lightly grease a 9×13-inch baking dish.
Heat olive oil in a large skillet. Season chicken with garlic powder, onion powder, paprika, salt, and pepper. Sear for 5–6 minutes until lightly golden. Add broccoli during the last 2 minutes to soften. Transfer both to the baking dish.
In the same skillet, melt butter over medium heat. Stir in flour and cook for 1–2 minutes until lightly golden to make a roux.
Slowly whisk in milk and chicken broth until smooth. Cook 3–5 minutes until the sauce thickens.
Lower heat and stir in 1½ cups cheddar cheese, Parmesan, and optional mustard and nutmeg until melted and creamy.
Pour the sauce evenly over the chicken and broccoli, stirring gently to coat.
Top with remaining cheddar and mozzarella. Mix Panko with melted butter and sprinkle on top.
Bake uncovered for 20–25 minutes until bubbly and golden brown.
Let rest for 5–10 minutes before serving for easier slicing.