Heat the vegetable oil in a heavy skillet over medium-high heat. Add the meatballs and brown them on all sides (you may have to brown the meatballs in batches). Adjust the heat so that they get nice and brown, not burned. Drain on paper towels.
Meanwhile, bring the broth to a boil in a large pot over high heat, Stir in escarole, cannellini beans, remaining garlic and pepper flakes. Taste for seasoning and add salt and freshly ground pepper. Lower the heat to a simmer. Add the cooked meatballs. Deglaze the the meatball pan with a little chicken broth and add that back to the soup pot. Let the soup simmer for about 10 minutes. Stir in the shredded basil just before serving. Pass additional Parmesan cheese and red pepper flakes.