In a large pot of boiling water, add the escarole and cook until it wilts (this removes the bitter taste from the greens). Remove from heat and strain the greens from the water. When cooled, squeeze out all excess liquid.
In a separate pot over medium heat, bring the broth to a boil. In a separate large bowl, combine the ground beef, 1 egg, breadcrumbs, basil, parsley and 1/2 cup Parmesan cheese. Mix well and form into bite-size balls. Drop the balls into the broth. When they rise to the top, they are cooked.
Add the escarole to the broth. In a separate bowl, combine the remaining 3 eggs with the remaining 1 cup of cheese. Pour this mixture into the soup, stirring continuously, until the egg is cooked.