Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Whisk egg and water together in a bowl. Mix in bread crumbs and let stand 5 minutes. Add turkey, Parmesan cheese, parsley, garlic, salt, and pepper; stir gently to blend. Shape mixture into 1 1/4-inch diameter meatballs using wet hands. Place meatballs on the prepared baking sheet. Cover with plastic wrap and refrigerate until firm, 15 to 30 minutes.
Coat chilled meatballs in 1 tablespoon olive oil.
Bake in the preheated oven until browned, about 20 minutes.
Pour remaining olive oil into a heavy soup pot over medium heat. Add carrots and shallot; cook until tender, about 5 minutes. Add chicken broth and wine. Bring to a boil, add orzo, and reduce heat to medium. Cook, uncovered, until orzo is tender, about 5 minutes. Add kale and cook until wilted, about 5 minutes more. Add cooked meatballs and cook until heated through, about 5 minutes. Season with salt and pepper.
