Preheat oven to 400 degrees F. Coat a 13- x 9-inch or other large baking dish with nonstick cooking spray.
Place the chopped broccoli in a small microwavable dish and add ¼ cup water. Cover the bowl with a paper towel and cook on HIGH power for 1 minute. Carefully drain the water from the dish and set it aside.
Place a layer of plastic wrap over each piece of chicken and lightly pound with a mallet, if necessary, to ensure all pieces are about ¼-inch thick.
In a small bowl, combine the ricotta cheese, Swiss cheese, cooked and slightly cooled broccoli, salt and pepper. Set aside. Pour the panko bread crumbs into a shallow dish (like a pie plate). Place the eggs in a separate shallow dish and beat lightly with the mustard.
To assemble the stuffed chicken breasts, place about ¼ of the broccoli cheese filling (about 2 to 3 tablespoons) on the end of a piece of chicken and roll it up. Set it in the dish of beaten egg and carefully turn to coat. Allow the excess egg to drip off then place the chicken roll in the bread crumbs. Toss the bread crumbs over the chicken roll until well coated. Transfer the breaded chicken to the prepared pan and place it seam side down. Stuff and bread the remaining chicken and transfer them to the baking dish.
Bake uncovered for 35 to 40 minutes or until the chicken is cooked through and the internal temperature reads at least 165 degrees F when tested with an instant read thermometer. If you'd like to brown the coating more, set the oven to BROIL for a minute or two at the end of the cooking time.
Meanwhile, in a small saucepan over LOW heat, whisk the soup with the milk until smooth and cook until warmed through. Stir in the juice of half a lemon and season with salt and pepper, to taste. Remove from the heat.
Spoon about half the warmed gravy over the cooked chicken in the baking dish. Transfer the remaining gravy to a gravy boat or small bowl and serve it with the chicken.