Bring a large pot of water to a boil. Add the soba noodles and the salt and cook until the noodles are cooked through, 2 to 3 minutes. Strain through a medium mesh sieve and rinse the noodles under cold running water for 1 minute.
Meanwhile, make the broth. Bring the chicken broth, soy sauce, garlic, and ginger to a boil in a large saucepan over high heat. Reduce the heat to medium and simmer for 3 minutes, then add the mushrooms and simmer until they’re tender, about 5 minutes. Add 3/4 of the scallions and simmer until soft, about 1 minute.
Divide the noodles among 4 bowls and pour the soup over the noodles. Add the spinach, sprinkle with the remaining scallions and serve each bowl with a hard boiled egg half. Kampai!
*If you’re gluten intolerant or are making soba noodles for someone who is, be sure to read the ingredient list on the package. Sometimes wheat flour is mixed in with buckwheat flour.