Heat oil in a large heavy bottom soup pot over high heat. Add chicken and sprinkle all over with salt. Sear, until golden and comes free without sticking, 4 to 6 minutes. Flip the chicken over and let cook on the other side until browned, about 3 minutes. Set chicken aside on a plate (It will continue cooking in a later step.)

Meanwhile, bring a medium saucepan of water to a boil over high heat. Once boiling, lower eggs, one at a time into the pot with a slotted spoon. Set timer for 6 minutes. Drain off water and run cold running water over the eggs for two minutes. Set aside.

Add shallot and shiitake mushrooms to the hot oil in the pot and cook, stirring constantly until the mushrooms are wilted and the shallots are starting to brown, about 3 minutes.

Add broth, star anise (or 5-spice), ginger, tamari, mirin, pepper flakes and the chicken and juices and bring to a simmer over high heat. Reduce heat to maintain a gentle simmer and cook, until the chicken is cooked through, about 4 minutes.

Transfer the chicken to a cutting board and chop. Add the chopped chicken back to the soup.

Increase heat to high, add ramen noodles and bok choy to the soup. Cover and bring to a simmer, stirring occasionally. Reduce heat to maintain a simmer and cook until the ramen is soft and the bok choy is crisp-tender, 2 to 4 minutes.

Remove from the heat. Discard star anise. Ladle a half cup of the broth into a heat proof measuring cup or bowl. Whisk in miso paste and then stir it back into the soup.

To serve: Peel and cut the eggs in half. Use tongs to divide the noodle mixture among four large bowls. Arrange chicken and bok choy over the noodles. Pour the broth into the bowls. Top with eggs and scallions.