Heat sesame oil in large pot over medium; cook garlic and ginger about 1 minute until fragrant without burning.
Add broth; gently simmer over medium-high.
Meanwhile, whisk miso with about ½ cup hot broth in small bowl until smooth and lump-free.
Reduce to medium-low; return miso mixture with soy sauce.
Add tofu and greens; simmer 5-7 minutes until greens wilted and tofu heated through.
Off heat, add green onions; taste and adjust with more soy sauce or miso if needed.
Ladle into bowls; add optional seaweed and serve immediately while hot.