Combine stuffing mix and water in large bowl. Let stand 5 min. Meanwhile, pound chicken to 1/4-inch thickness. Add broccoli to stuffing; mix lightly. Spread onto chicken to within 1/2 inch of edges; roll up starting at one short end of each.
Place, seam-sides down, in 13x9-inch baking dish. Mix soup and milk; pour over chicken. Top with paprika and cheese.
Bake 30 min. or until chicken is done (165ºF).