Heat sesame oil in a large pot over medium heat. Add garlic and ginger; sauté until fragrant.
Add chicken breasts and sear lightly for 2–3 minutes per side.
Pour in chicken broth and water. Stir in soy sauce, miso paste, rice vinegar, and black pepper.
Bring to a gentle boil, then reduce heat and simmer for 15 minutes until chicken is fully cooked.
Remove chicken, shred with forks, and return to the pot.
Add ramen noodles and cook according to package instructions (about 3–4 minutes).
Stir in mushrooms and spinach during the last 2 minutes of cooking.
Divide into bowls, top with soft-boiled eggs, green onions, and chili oil. Serve hot.