Prep the oven and pan. Heat your oven to 375°F (190°C).
Grease a 9x13-inch baking dish with olive oil or butter.
Blanch or steam the broccoli. Cook the broccoli until crisp-tender, about 2–3 minutes in boiling water or 4–5 minutes in the microwave with a splash of water. Drain well and pat dry to prevent a watery bake.
Cook the chicken. In a large skillet over medium heat, warm 2 tablespoons olive oil. Add chicken, garlic powder, onion powder, smoked paprika, salt, and pepper.
Sauté 5–7 minutes until just cooked through and lightly golden. Do not overcook. Transfer to a plate.
Make the cheese sauce. In the same skillet on low heat, whisk together cream cheese, heavy cream, and chicken broth until smooth.
Stir in Dijon. When it simmers gently, add 1 cup cheddar, mozzarella, and Parmesan. Whisk until melted and glossy.
Taste and adjust salt and pepper.
Assemble. Spread the broccoli and chicken in the baking dish. Pour the cheese sauce evenly over the top and toss gently to coat. Sprinkle the remaining 1/2 cup cheddar over everything.
Add red pepper flakes if using.
Bake. Bake uncovered for 15–20 minutes, until bubbling at the edges and the top is melted and lightly golden.
Finish and serve. Let it rest 5 minutes so the sauce sets slightly. Garnish with parsley or chives. Serve warm.