Slice chicken breast meat into bite size pieces. Season with salt and pepper. Dust with 2 tablespoons flour and set aside.
Over medium high heat in a large skillet add 1 tablespoon of olive oil and brown the broccoli slightly, cooking for 3 minutes. Add 1/2 cup chicken broth and cover. Cook for 2 minutes. Remove from pan and set aside.
Add the other tablespoon of oil to the skillet and brown the chicken pieces over medium high heat. Cook for 8 minutes.
Place chicken in a 13x9" baking dish seasoned with cooking spray. Sprinkle broccoli on top of chicken.
In same skillet add the butter and over medium heat sauté the shallot for a minute. Sprinkle remaining 2 tablespoons of flour in pan and stir to cook. Add the Worcestershire sauce, sherry, chicken stock and half and half. Stir and reduce for several minutes until thickened. Stir in Parmesan cheese and pour over chicken and broccoli.
Sprinkle Panko breadcrumbs and more cheese (optional) if you like on top. Broil for 3-5 minutes until top is golden brown and bubbly. Serve with grated lemon zest over top (optional).