Prep the oven and dish: Preheat to 375°F (190°C). Lightly grease a 9x13-inch baking dish with cooking spray or butter.
Season the chicken: In a bowl, toss chicken pieces with olive oil, garlic powder, onion powder, smoked paprika, salt, and pepper.
Set aside.
Par-cook the broccoli: For fresh broccoli, steam or microwave for 2–3 minutes until bright green and just tender. For frozen, thaw and pat dry. This step helps avoid a watery bake.
Make the creamy sauce: In a medium bowl, whisk together cream cheese, sour cream, heavy cream, and chicken broth until smooth.
Stir in Dijon, Italian seasoning, 1 cup cheddar, mozzarella, and Parmesan. Season with a pinch of salt and pepper.
Assemble: Spread broccoli in the baking dish. Scatter seasoned chicken over the top.
Pour the cheese sauce evenly over everything, then gently toss to coat. Smooth into an even layer.
Top with cheese: Sprinkle the remaining 3/4 cup cheddar over the surface.
Bake: Place on the middle rack and bake for 25–30 minutes, until the chicken is cooked through (165°F/74°C in the thickest pieces) and the edges are bubbling.
Broil for color (optional): Switch to broil for 1–2 minutes to get a golden, bubbly top. Watch closely to avoid burning.
Rest and serve: Let the bake rest 5–10 minutes to thicken.
Garnish with parsley and serve hot.