Preheat oven to 350 degrees. Over low heat, warm milk, cream cheese and Worcestershire sauce in a nonstick saucepan and stir until smooth. Chop each breast into 10 or 12 pieces. Place the chicken and broccoli in a baking dish. Top with 1/2 cup of Cheddar cheese and the cream cheese sauce, and cover the dish with aluminum foil. Once the oven is preheated, bake for 25 minutes. Remove the dish from oven and sprinkle the remaining 1/4 cup cheese. Place dish back in oven and bake until the cheese is melted.