Add the chicken thighs and onions to a large pot and cover water by 1 inch. If desired, you can brown the thighs and onion in a bit of oil first. Season with salt and pepper.
Bring to a boil and then reduce heat and simmer, uncovered, for 2 hours until very reduced and the chicken is nearly falling off the bone. Bring to a low boil for 30 minutes more to allow the stock to further reduce and turn a deep golden brown.
Depending on the size of your pot and how much water there was, the time may vary. You want the liquid to reduce by about just shy of half, so you should have about 4 cups of rich liquid leftover.
Allow the stock to cool for about 40 minutes. If desired, remove the chicken from the broth and strain it through a sieve and discard the onions. Combine the stock and chicken in a bowl or air-tight storage container. Transfer to the refrigerator overnight.
Prepare the Soba Soup:
The next day, remove the chicken from the refrigerator. Set a medium pot on the stove over no heat. If there's excessive fat on top of the stock, skim it off and discard it but don't remove any of the gelatinous stock below!
Pick the chicken meat from the bones and add it to the pot. Discard the bones and pour the stock over the chicken.
Cook the Soba Soup:
Turn the heat on the pot to medium high. Once boiling, add the star anise pods, soy sauce, sesame oil, chili oil, and brown sugar. Reduce heat and simmer for 10 minutes.
Taste the soup and season to your preferences. If you need more liquid, add a splash of water. Bring the broth back to a boil and add the soba noodles and cook until tender, 6-8 minutes. Turn off the heat.
Serve the soup as soon as the noodles are al dente. Ladle into bowls and drizzle with more chili oil. Garnish with dry chives or scallions, fresh scallions, or a sprinkle of sesame seeds. For additional heat, garnish with a drizzle of chili oil. Enjoy!
You can add a variety of aromatics to your stock. I like to keep it simple for this recipe!