In a small bowl, stir together the miso, sesame oil, and ginger. Set it aside.
Melt the coconut oil or olive oil in a large saucepan over medium-high heat. Stir in the green onions, mushrooms, and carrots, and cook until softened, about 5 minutes.
Add the broth and bring it to a simmer. Partially cover the pan and cook for 10 minutes, then turn off the heat. Add in the spinach right away so it can begin to wilt, then scoop out 1/2 cup of broth to add to the miso mixture.
Whisk the miso until smooth, then add it into the pot of soup, along with the tamari. Taste and adjust any seasoning to your liking, then serve warm. This soup is best served the day it's made, but you can store it for up to 4 days in the fridge. (Reheating may destroy some of the probiotics in miso, but it still tastes good!)