Pound chicken breasts to 1/4-1/2 inch thickness. Place a cheese and ham slice on each breast. Roll the chicken up over the ham and cheese and secure with toothpicks (or butcher's twine). Mix the breadcrumbs and paprika in a small bowl. Coat the chicken with melted butter, then roll in breadcrumbs until completely covered.
Heat the butter in a large skillet over medium-high heat, and cook the chicken until browned on all sides. Add the broth and bouillon. Reduce heat to low, cover, and simmer for 30 minutes, until chicken is no longer pink and juices run clear.
Remove the toothpicks, and transfer the breasts to a warm platter (leave any leftover broth liquids in the skillet).
For the sauce:
Blend the cornstarch with the cream in a small bowl, and whisk slowly into the skillet (if JUST making the sauce, bring butter, broth and bouillon to a simmer in a medium-sized pot and reduce for 10-15 minutes, then add the cornstarch/cream mixture). Cook, stirring until thickened, then add the pepper and basil.
Return the chicken to the skillet, top with any remaining Swiss cheese, and simmer an additional 10 minutes on low heat.