Heat sesame oil in a medium soup pot over medium heat. Add garlic and ginger and sauté for about 30 seconds until fragrant.
Pour in the broth and bring to a gentle simmer.
Add noodles to the pot and cook according to package instructions until just tender.
In a small bowl, whisk miso paste with a few tablespoons of hot broth until smooth. Reduce heat to low and gently stir the miso mixture into the soup.
Add soy sauce, mushrooms, and spinach or bok choy if using. Simmer gently for 2–3 minutes until vegetables are tender.
Taste and adjust seasoning if needed. Remove from heat and garnish with green onions. Serve warm.