Preheat your oven to 375°F (190°C). Spray a 8 x 9 inches baking dish with cooking spray to prevent sticking.
In a large skillet, melt the butter over medium heat. Once melted, add the flour and whisk until combined. Cook for 2-3 minutes, or until the mixture becomes bubbly and golden in color.
Slowly whisk in the chicken broth, ensuring there are no lumps. Follow by adding the milk, while stirring constantly to maintain a smooth consistency. Continue cooking the sauce until it thickens and starts bubbling.
Remove the skillet from heat and stir in the sour cream Dijon mustard, salt, garlic and onion powder, combining well.
Place the broccoli in a microwave-safe bowl with 2 tablespoons of water. Cover the bowl and microwave on high for 2 minutes. Drain the broccoli to remove any excess water.
Add the partially cooked broccoli and the chicken to the skillet with the sauce. Stir everything together until well combined.
Transfer the mixture from the skillet into the prepared baking dish, spreading it out evenly.
In a small bowl, mix together the cheese and bread crumbs. Sprinkle this breadcrumb mixture evenly over the top of the chicken and broccoli.
Place the baking dish in the preheated oven and bake for 20-25 minutes, or until the cheese and bread crumbs turn golden brown and crispy, and the sauce is bubbling.
Once done, remove the dish from the oven and let it cool for a few minutes before serving.