In a large bowl, mix together minced beef, green onions, corn starch, and pepper. Gather meat in hand and throw against the side of the bowl for about 3 to 4 minutes. Meat will come together in a ball. Shape into 1¼-inch diameter meatballs.
Bring chicken stock to boil in a large pot. Add meatballs and season with salt and pepper. Allow meatballs to cook for about 10 minutes. Skim off scum.
In the meantime, boil soba in another pot for about 5 minutes or according to packaging instructions. Remove and drain. Divide into 4 bowls.
Add kale to beef ball soup. Boil for 3 to 4 minutes or until kale turns a bright green color. Do not overcook the kale.
Turn off heat. Spoon beef balls, kale, and soup over soba. Garnish with sesame oil, bonito shavings, and togarashi. Serve immediately.