Pound chicken breasts as thin as possible without completely destroying the chicken (about 1/2" thick). Roll up the cheese in the ham.. kind of how you would roll up a burrito (folding in the ends over the cheese, then rolling it up) this will keep the cheese from oozing out. Now roll up the ham and cheese in the chicken. Keep it all together using toothpicks.
Place the melted butter in a shallow bowl or dish. In a separate shallow dish, mix the Panko, Parmesan cheese and paprika. Dip each chicken in the butter, then roll in the bread crumb mixture.
Heat the remaining butter (1/4 c.) in a large skillet over medium-high heat, and cook each chicken until browned on all sides. Place on a plate until remaining chicken is browned. When all the chicken is browned, add a little more butter (or cooking spray) to the bottom of the pan to keep chicken from sticking. Place ALL the chicken back in the skillet. Sprinkle paprika, to taste, over the chicken, then add chicken broth to the pan (don't pour the broth over the chicken, try to pour it directly into the bottom of the pan). Reduce heat to low, cover, and simmer for 15-20 minutes, until chicken is no longer pink and juices run clear.
Transfer the chicken cordon bleus to a warm platter and remove toothpicks. The broth it was sitting in should have reduced and thickened a little during cooking. Add salt, pepper, and paprika to taste. Whisk in heavy cream. Cook, stirring until thickened, and pour over the chicken. Serve and enjoy!