Heat oil in a large pot over medium heat.
Add chicken and cook for 3 to 4 minutes, until lightly cooked on the outside.
Add garlic and ginger. Stir for 30 seconds until fragrant.
Pour in chicken broth, soy sauce, and sesame oil.
Bring to a gentle simmer. Cook for 5 to 7 minutes, or until the chicken is cooked through.
Add carrots and mushrooms. Simmer for 3 to 4 minutes.
Add ramen noodles and cook for 2 to 4 minutes, or until tender.
Stir in spinach or bok choy during the last minute of cooking.
Taste the broth and add lime juice, rice vinegar, chili oil, or more soy sauce if needed.
Serve hot with green onions, soft-boiled eggs, sesame seeds, and chili oil if desired.