Heat the sesame oil in a large pot over medium heat. Add the grated ginger and minced garlic and cook for one minute until fragrant.
Pour in the vegetable broth and bring it to a gentle simmer.
Add the sliced carrots and mushrooms. Cook for 5 minutes until the carrots begin to soften.
Stir in the tofu cubes and continue simmering for another 3 minutes.
Place the miso paste in a small bowl and ladle in about half a cup of the hot broth. Stir until the miso dissolves completely, then return the mixture to the pot.
Add the baby spinach and cook for 1 minute until it wilts. Remove the pot from the heat.
Divide the soup among bowls and top each serving with sliced green onions.