For the Soba: Combine the chickpea Miso, green tea, ginger, garlic, lime, coconut aminos and mushrooms in a small saucepan and bring to a boil. Reduce heat and simmer for 5 minutes. While the sauce is simmering, prepare the soba according to the package’s instructions.
For the Carrots: Heat the sesame oil in a medium skillet. Add the carrots and cook for 3 minutes. Add the water and continue cooking the carrots until they are slightly soft, approximately 5 minutes (this may vary depending on the size of your carrots). Drizzle the honey over the carrots and add the salt and a generous amount of cracked pepper, toss the carrots to coat evenly and cook an additional 2 minutes.
To Serve: Transfer the pasta to a bowl and pour the miso sauce over the noodles until covered (you won’t use all of the sauce). Top with the glazed carrots and garnish with the black sesame seeds.