In a large pot, bring the vegetable broth to a simmer over medium heat.
Add the miso paste, soy sauce, sesame oil, grated ginger, and minced garlic to the broth. Whisk until the miso is fully dissolved.
Stir in the sliced mushrooms and julienned carrot. Cook for about 5 minutes, until the vegetables are tender.
Meanwhile, cook the soba noodles according to package instructions. Drain and set aside.
Add the baby spinach to the broth and cook for an additional 2 minutes until wilted.
Divide the cooked soba noodles into bowls and ladle the hot soup over the noodles.
Garnish with sliced green onions and sesame seeds before serving.