Preheat the oven to 400° and lightly spray a 9x13 baking dish with a non-stick cooking spray. Set aside.
Pound each chicken breast, in between plastic wrap or parchment paper, until thin with even thickness.
Place two pieces of cheese on each chicken breast, followed by ½ cup of broccoli. Tightly roll chicken up and place on a plate, seam side down. Repeat with the remaining chicken.
Set up the dredging station with three shallow bowls or containers.
In the first bowl, add flour, and in the second bowl, whisk eggs and buttermilk together.
In the third bowl, whisk breadcrumbs and seasonings together.
Roll one chicken breast at a time into the flour, then the egg mixture and lastly, the breadcrumb mixture.
Place coated chicken into the prepared baking dish seam side down.
Bake for 45-50 minutes or until the internal temperature reaches 165° then carefully remove from the oven.
While the chicken is baking, make the sauce.
In a skillet or frying pan, melt butter then stir in flour until combined. Cook for 1-2 minutes over medium heat.
Slowly whisk milk into skillet and stir until sauce comes together.
Add Parmesan cheese and garlic powder, stir constantly until cheese is melted then add Dijon mustard.
Simmer sauce until thick enough to coat the back of a spoon.
Pour sauce over chicken and enjoy with your favorite side dishes.