Place eggs in a shallow bowl. Place flour in a shallow bowl. In another shallow bowl, combine both bread crumbs with salt and pepper to taste.
Coat chicken with flour. Then dip in egg, then coat with breadcrumb mixture.
In a skillet over medium heat, fry chicken in butter, on both sides, until the juices run clear, about 15 minutes. Remove from skillet and keep warm.
Add the broth to the skillet; bring to a boil over medium heat. Stir and scrape to loosen browned bits from pan.
Stir in the cream and pimentos (If using dried basil add this now); boil and stir for one minute. Reduce heat; add the Parmesan cheese, basil and black pepper to taste. Simmer and stir until heated through. To serve, pour the sauce over the chicken.