In a large pot, heat the sesame oil over medium heat. Add the minced ginger and garlic, sautéing for about 2 minutes until fragrant.
Pour in the chicken or vegetable broth and bring to a simmer.
Stir in the miso paste and soy sauce, mixing well until the miso is fully dissolved.
Add the ramen noodles to the pot and cook according to package instructions, usually about 4-5 minutes.
In the last 2 minutes of cooking, add the chopped bok choy and sliced shiitake mushrooms to the pot.
While the ramen is cooking, bring a small pot of water to a boil. Gently add the eggs and boil for 6-7 minutes for a soft-boiled egg. Remove and place in an ice bath to cool, then peel.
Once the noodles and vegetables are cooked, taste the broth and adjust seasoning with salt and pepper as needed.
Serve the ramen in bowls, halving the soft-boiled eggs and placing them on top. Garnish with chopped green onions and sesame seeds.