Preheat oven to 425 degrees F. Prepare a 9x13" baking dish with non-stick cooking spray and set aside.
Lay sliced chicken breasts flat on a cutting board. Sprinkle each with salt and pepper. Top each chicken breast with 1 ounce of shredded Cabot Vermont Sharp Cheddar Cheese. Top that with 1/4 cup of the cooked, chopped broccoli. Bring both sides of the chicken breast around filling and secure with toothpicks.
In a shallow bowl, beat the two eggs. In a separate shallow bowl, combine the melted butter and breadcrumbs, stirring to moisten breadcrumbs with the butter.
Dip each prepared chicken breast in the egg mixture, gently rolling to coat the chicken.
Gently roll chicken in moist breadcrumbs to coat. Place in prepared baking dish.
Bake at 425 degrees F. for 25 minutes, until juices run clear, breadcrumbs are golden and chicken is done. Remove from oven and top each portion with the remaining cheese, evenly divided.
Return pan to oven for no more than 5 minutes to melt the cheese. Remove from oven and serve.