Bring a medium pot of water to a boil. Add the soba noodles and cook them according to the package directions. Drain the noodles in a colander and rinse them under cool water.
While the noodles cook, coat the bottom of a large pot with a tablespoon of the oil and place it over medium heat. Give the oil a minute to heat up, then add the garlic, ginger, and white parts of your scallions. Sauté the aromatics for about a minute, until very fragrant, stirring constantly.
Add the water to the pot. Raise the heat and bring it to a boil.
Cook the tofu while the water heats up. Coat the bottom of a medium nonstick skillet with the remaining tablespoon of oil and place it over medium-high heat. Give the oil a minute to heat up, then add the tofu. Cook the tofu for 8 to 10 minutes, flipping the pieces once or twice, until golden brown and crispy. Move them to a plate when done.
Once the water in the pot boils, add the carrots and simmer them for about 2 minutes, until bright orange and just tender.
Stir in the spinach, then remove the pot from heat. Ladle about ½ cup of water from the pot into a small heatproof cup and stir or whisk in the miso until fully dissolved. Pour the miso mixture into the pot. Stir until the miso is dissolved and the spinach is fully wilted. Add 2 tablespoons of soy sauce, plus more to taste.
Stir in the noodles (Note 1), tofu, and sesame oil.
Ladle the soba noodle soup into bowls and top with sesame seeds and the green parts of your scallions.