Blend beef, 1/3 cup cheese, breadcrumbs, egg, garlic, salt, and pepper in medium bowl. Using moistened hands, shape meat mixture into 3/4 inch meatballs.
Heat 1 1/2 cups broth and oil in a large pot over medium-high heat. Add meatballs and simmer until firm enough to hold shape, about 5 minutes. Using slotted spoon, transfer meatballs to bowl. Boil broth until reduced to glaze, about 6 minutes. Add celery and onion to pot. Stir until vegetables are soft, about 5 minutes. Add remaining 6 cups broth, pasta and meatballs with any juices. Reduce heat. Simmer until pasta is tender, about 10 minutes. Add escarole and simmer until wilted, about 5 minutes. Season with salt and pepper. Ladle soup into bowls. Serve with remaining 1 cup cheese.
** I make my pasta seperate and add to the individual soup bowls later. I like my pasta al dente.