In a medium pot, combine 6 cups chicken broth, 2 cloves garlic (smashed), and 1-inch piece fresh ginger (thinly sliced); bring to a gentle simmer over medium heat and cook for 10 minutes.
While broth simmers, place 2 large eggs in boiling water and cook for 6–7 minutes; transfer eggs to an ice bath, cool, peel, and set aside.
Strain out and discard the garlic and ginger from the broth.
Stir 0.25 cup soy sauce and 2 tablespoons mirin into the broth (or use 1 teaspoon sugar and 1 tablespoon rice vinegar as an optional alternative).
Add 4 ounces sliced cremini mushrooms to the broth and simmer for 3–5 minutes until tender.
Stir in 2 cups fresh spinach and cook 1 minute until wilted; taste and adjust soy sauce if desired.
In a separate pot, boil water and cook 4 blocks dried ramen noodles (without seasoning packets) for 3–4 minutes until al dente; drain well.
Divide cooked noodles evenly between 2 bowls and ladle the hot broth with mushrooms and spinach over them.
Slice each soft-boiled egg in half and place two halves atop each bowl.
Garnish each bowl with sliced green onions and a light drizzle of sesame oil just before serving.