In a large pot, add the coconut milk, shallots, lemongrass, ginger, 2 Thai chilies - or one bird’s eye chili, and the water. Bring it to a light simmer, cover and cook for 20 minutes.
While the soup is cooking, cook the soba noodles. Bring a large pot of water to a boil (about 6 cups of water), and drop the soba into the pot. Stir so they don’t stick together, and cook for 5-7 minutes. When cooked, pour the noodles and water into a strainer or colander, and run under cold water to cool and stop cooking. Set aside.
Place a mesh strainer over another pot (large enough to hold the coconut broth), and pour the soup into the pot, straining out the cooked vegetables. Toss out the cooked vegetables, and pour the broth back into the original pot. Bring to a light simmer and add the mushrooms, bok choy, and the remaining chili. Cook another 10 minutes. Remove from heat, and then add the soy sauce and lime juice. Stir well and season to taste with more tamari or lime if necessary. Serve over soba noodles.