Place all of the ingredients for the sauce in a small saucepan over medium heat. Bring to a boil and then reduce heat to simmer for 10 minutes.
Meanwhile, combine the milk and egg in a dish and beat well to combine. Place the panko and black pepper in another shallow dish.
Place the chicken in the egg mixture and then press into the panko mixture. Repeat with remaining chicken.
Heat 1 tablespoon olive oil in a large skillet. Cook the chicken over medium heat for 4-5 minutes per side or until it is fully cooked.
Add the broccoli and sesame seeds to the skillet and then add half of the sauce. Toss to coat and then heat for 1-2 minutes.
Serve the chicken and broccoli with additional sauce on the side.