In a bowl, combine the turkey, egg white, parsley, onion, half of the garlic, salt, and pepper and fluff with a fork. Shape into balls the size of walnuts (about 24 meatballs).
In a large nonstick skillet over medium heat, cook the meatballs until cooked through, crispy, and golden, about 5 minutes. Using a slotted spoon, transfer the meatballs to a paper towel-lined plate.
In a soup pot over medium-high heat, add the oil, remaining garlic, and shallots and cook until translucent and soft, about 5 minutes. Add the chicken stock and simmer. Add the thyme, meatballs, and pasta and return to a simmer. Stir in the escarole and salt and pepper to taste. Ladle into 4 deep soup bowls and serve.