Prep the oven and pan. Preheat oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish with olive oil or butter.
Cook the broccoli. Steam or blanch the florets until crisp-tender, about 3–4 minutes fresh or 4–5 minutes from frozen. Drain well and pat dry to avoid a watery casserole.
Build the sauce base. In a large skillet over medium heat, melt the butter. Add garlic and cook 30 seconds until fragrant.
Make it creamy. Whisk in heavy cream and chicken broth.
Add cream cheese in pieces and stir until fully melted and smooth.
Season and thicken. Stir in Dijon, onion powder, smoked paprika, 1 cup shredded cheddar, and all the Parmesan. Simmer 2–3 minutes until the sauce slightly thickens. Taste and season with salt and pepper.
Combine the filling. In a large bowl, mix cooked chicken and broccoli.
Pour the sauce over and fold until everything is evenly coated.
Assemble. Spread the mixture into the prepared baking dish. Top with the remaining 1 cup cheddar.
Bake. Place in the oven for 18–22 minutes, until bubbly around the edges and the top is melted and lightly golden.
Rest and serve. Let it rest 5–10 minutes so the sauce sets. Spoon into bowls and season with extra pepper if you like.