In a large saucepan or Dutch oven, heat the sesame oil over medium heat.
Add the sliced green onions, grated ginger, and minced garlic.
Sauté for 2 minutes until fragrant, stirring frequently.
Pour in the 4 cups (960 ml) of water and add the black pepper.
Bring the mixture to a rolling boil.
Add the broken soba noodle pieces, return to a boil, then reduce the heat to a simmer.
Cook, uncovered, for 5 minutes.
While the noodles cook, prepare the miso slurry.
In a small bowl, whisk together the 1/2 cup (480 ml) of hot water, miso paste, and tahini until smooth and fully combined.
Stir the smooth miso mixture into the soup. Gently add the cubed tofu and shredded seaweed.
Continue to simmer for 1 to 2 more minutes, just until everything is heated through. Be careful not to boil the soup after adding the miso.