Place the dried mushrooms in a bowl, pour the cup of boiling water over, cover, and let stand 10 minutes.
While the mushrooms are soaking, simmer the onions, garlic, and ginger in the vegetable broth for 5 minutes. Add the tofu (if using) and simmer 5 more minutes. Stir in the rice wine, vinegar, tamari, minced jalapeño, cayenne, and sesame oil.
Strain the soaking liquid from the dried mushrooms into the soup. Slice the mushrooms into slivers and add them.
Dissolve the arrowroot in the 1/4 cup of cold water. Add to the soup and bring to a gentle boil, stirring. The soup will become very slightly thickened.
Place the miso in a bowl and mash in 1/2 cup of the soup until smooth. Add the miso liquid to the soup along with the carrots. Heat but do not allow the soup to boil--boiling destroys some of the nutrition of the miso and changes the flavor. Taste the soup and adjust the seasoning with more vinegar, tamari, or cayenne, as needed. Serve immediately.