Bring a pot of water to a boil. Carefully lower 4 eggs into the water and boil for exactly 6 minutes and 30 seconds. Immediately transfer to an ice bath, peel, and set aside.
Season chicken breasts with salt and pepper. In a hot pan with a splash of oil, sear the chicken for 6-7 minutes per side until the internal temperature reaches 165°F (74°C). Let rest for 5 minutes before slicing.
In a large pot, heat sesame oil over medium heat. Sauté minced ginger and garlic for 1-2 minutes until fragrant.
Whisk in the miso paste, soy sauce, and mirin. Gradually pour in the chicken bone broth and bring to a gentle simmer.
Add the halved bok choy to the simmering broth for 3 minutes until tender-crisp, then remove and set aside.
Cook the ramen noodles in a separate pot of boiling water according to package instructions. Drain thoroughly.
Divide the cooked noodles between two large bowls. Pour the hot miso broth over the noodles.
Top each bowl with one sliced chicken breast, two halved soft-boiled eggs, the blanched bok choy, scallions, nori strips, and a drizzle of chili oil.