Pat the chicken thighs dry and season with salt. Heat the oil in a large pot over medium-high heat and sear the chicken, skin-side down, until golden brown, about 5 minutes.
Add the ginger and garlic and cook for 1 minute until fragrant. Pour in the water, scraping up any browned bits.
Bring to a gentle simmer (not a hard boil) and cook for 30 minutes, skimming off any foam, until the chicken is tender.
Remove the chicken and shred the meat, discarding bones and skin. Strain the broth and return it to the pot.
Whisk the miso paste with a ladleful of hot broth until smooth, then stir back into the pot along with the soy sauce. Add the shredded chicken.
Cook the ramen noodles separately according to package directions. Divide noodles among bowls, ladle over the hot broth and chicken, and top with soft-boiled eggs, green onions, nori, and a drizzle of sesame oil.