In a medium bowl, mix together the turkey, eggs, garlic, onion, bread crumbs, Parmesan, parsley, 1/2 teaspoon of the salt, and the black pepper until thoroughly combined.
Shape the mixture into twenty meatballs.
In a large frying pan, heat 11/2 tablespoons of the oil over moderate heat. Add half the meatballs to the pan and cook, turning, until browned on all sides, about 3 minutes.
Remove the meatballs from the pan and drain on paper towels. Repeat with the remaining 11/2 tablespoons oil and the rest of the meatballs.
Put all of the meatballs, the escarole, broth, water, vinegar, red-pepper flakes, and the remaining 1 teaspoon of salt in a large pot.
Cover and bring to a simmer over moderate heat, stirring occasionally. The meatballs should be cooked through by the time the broth comes to a simmer.