Gently stir together ground chicken, scallions, ginger, garlic, and 2 tablespoons tamari in a mixing bowl. Form into 1-inch diameter meatballs, about 1½ tablespoons per meatball.
Heat oil in a large skillet over medium-high heat. Add meatballs and cook until brown all over, about 10 minutes. Transfer meatballs to a plate lined with paper towels to soak up excess cooking oil.
Turn down heat under skillet to medium. Add a little extra cooking oil if necessary, then add sliced bok choy, cooking until slightly charred. Remove bok choy to plate and cook shiitake mushrooms. Divide Ginger Scallion Meatballs, baby bok choy, shiitake, and soba noodles among serving bowls.
In a separate pot, heat chicken stock. Season stock with 2 tablespoons tamari, taste, and adjust with more tamari or sea salt. Tamari will add extra umami and make the soup darker, salt will only make the soup saltier and keep the broth a lighter color.
Ladle boiling hot stock into serving bowls over meatballs, vegetables, and noodles. Drizzle each bowl with 1 teaspoon toasted sesame oil. Serve along with sliced scallions, toasted sesame seeds, chili sambal.