In a soup pot on medium heat, cook the ginger, garlic and cayenne in the oil for a minute before adding the onions and salt. Cover and cook, stirring often, until the onions soften, about 5 minutes.
Stir in the cabbage and sweet potatoes. Add about 3 1/2 cups of the broth. Cover and increase the heat to bring to a boil. Then reduce the heat and simmer for 15 minutes.
In a bowl, whisk together the peanut butter and the remaining 1/2 cup of broth until smooth. Add the peanut butter to the soup with the tomatoes and soy sauce. Simmer covered until the vegetables are tender, about 5 minutes.