Prepare the ingredients for the soup while the mushrooms are soaking. Remove mushrooms from water, reserving the liquid, and thinly slice.
In a large pot, heat ghee over medium heat and add bacon, shallots, garlic, ginger, and lemongrass. Stir frequently until fragrant, about 3 minutes. Add miso paste and stir for 2 more minutes. Add dried mushrooms and coconut aminos, scraping the bottom of the pan, then immediately add the bone broth and mushroom soaking liquid to the pot. Bring to a boil. Reduce heat and add black pepper. Cover and simmer until flavors have blended, about 20 minutes.
While soup is cooking, heat 2 additional pots with water, one for the noodles and one for the soft boiled eggs. Cook noodles according to the manufacturer's instructions. For the eggs, bring water to a boil and gently add the eggs. Cook eggs for 6½ minutes, then place into ice water to stop cooking. Peel, halve, and set aside.
Strain soup, discarding everything but the broth, and return broth to the pot. When ready to serve, add mushrooms to the pot and ladle soup into individual bowls. Add noodles, ½ egg per bowl, scallions, and seaweed. Serve immediately.
