Chef John's Italian Wedding Soup

Heat 2 teaspoons vegetable oil in a large, heavy pot over high heat. Add beef shank slice; cook until seared and browned on both sides, about 3 minutes per side. Add water, onion, carrot, celery, 3 cloves peeled garlic, bay leaf, and black peppercorns; bring to a simmer. Reduce heat to low; simmer until beef shank meat falls off the bone and stock turns brown in color, 4 to 5 hours. Add more water if beef stock level gets below about 5 cups.

Freeze short ribs until firm and very cold, about 15 minutes. Cut short rib meat into cubes; return to freezer until almost frozen, about 30 minutes more.

Whisk cream, egg, parsley, and 2 cloves minced garlic in a bowl. Stir in bread crumbs and 1/4 cup Parmigiano-Reggiano cheese.

Combine partially frozen beef rib cubes, 1/3 teaspoon salt, and 1/8 teaspoon black pepper in the bowl of a food processor; pulse until beef is coarsely ground, 5 to 10 pulses. Pulse in bread crumb mixture until mixture finely ground, about 5 pulses more. Transfer beef mixture to a bowl, cover with plastic wrap, and refrigerate.

Meanwhile, strain beef stock into a large soup pot; discard beef shank and vegetables. Stir chicken broth into beef stock; whisk in tomato paste. Bring broth mixture to a simmer; season with salt and black pepper. Stir in kale; simmer until tender, about 15 minutes.

Roll beef mixture into 2 teaspoon-sized meatballs.

Cook pastina in simmering soup for 5 minutes; gently add meatballs. Simmer until meatballs are cooked through and tender, about 15 minutes. Garnish servings with shredded Parmigiano-Reggiano cheese and black pepper.