Combine the ground turkey, breadcrumbs, egg, minced garlic, thyme, 2 tablespoons parsley, salt, and pepper in a mixing bowl. Mix until just combined, then form into 1-inch meatballs.
Heat the olive oil in a large pot over medium heat. Add the meatballs and cook for 5 to 6 minutes, turning occasionally until lightly browned on all sides.
Add the onion, carrots, parsnips, and sweet potato to the pot. Stir and cook for 3 minutes to soften the vegetables slightly.
Pour in the chicken broth and bring the soup to a simmer. Reduce heat to low, cover, and cook for 20 minutes until the meatballs are cooked through and the root vegetables are tender.
Taste and adjust salt if needed. Ladle into bowls and top with the remaining chopped parsley before serving.