Preheat oven to 350°F. Pluck florets off of stem of broccoli and discard stem (or cut very small). Combine cream cheese with 1 1/4 cups mozzarella cheese and broccoli florets. Roll into 1 inch diameter balls.
Place 2 chicken breast halves in large freezer-weight resealable plastic bag. Pound chicken with side of heavy can, rolling pin or meat mallet until chicken is 1/4-inch thick. Repeat with remaining chicken breast halves, adding 2 at a time to bag.
Place ranch dressing in a bowl, dip chicken in dressing until lightly covered. Put bread crumbs on a plate. Place chicken, top-sides down, in plate with bread crumbs. Put a stuffing ball in the middle of the chicken.
Starting at one of the narrow ends, tightly roll up chicken. Place, seam-sides down, in 13x9-inch baking dish. Repeat with remaining pounded chicken breast halves.
Bake 40 min. Sprinkle with remaining 3/4 cup cheese. Bake an additional 5 min or until chicken is cooked through (170°F) and cheese is melted.