Chop the sweet potato into small chunks. Thinly slice the leeks. Quarter the mushrooms.
Sauté the sweet potato and leeks in a soup pot, using ¼ cup of the vegetable broth as the cooking liquid. Cook for 10 minutes.
Add the remaining vegetable broth, miso, tahini, and cayenne. Cover and let simmer for 20 minutes.
Reserve ⅓ of the sweet potato chunks, then transfer the remaining liquid to a food processor. Blend until completely smooth.
Return the blended soup as well as the reserved sweet potato chunks to the pot. Add the quartered mushrooms and cook until the mushrooms are soft, about 5 minutes.
Remove from the heat and serve. Top with additional mushrooms, if desired, and sprinkle with salt and pepper. Enjoy!