Spray a 10-inch skillet with the cooking spray and heat over medium-high heat for 1 minute. Add the chicken and cook for 10 minutes or until well browned on both sides.
Add the broth, garlic and broccoli to the skillet and heat to a boil. Reduce the heat to low. Cover and cook for 5 minutes or until the chicken is cooked through. Remove the chicken from the skillet, cover and keep warm.
Stir the flour, milk, mustard and black pepper in a small bowl until the mixture is smooth. Add the flour mixture to the skillet. Cook and stir until the mixture boils and thickens. Serve the sauce with the chicken and noodles.