Step 1
Heat the olive oil in a large soup pot. Add the garlic and onions and cook over moderate heat, stirring occasionally, until softened, about 12 minutes. Add the ginger and andouille and cook for 5 minutes, stirring occasionally. Add the tomatoes and their juices; bring to a boil. Add the stock and kale; return to a boil.
Step 2
Reduce the heat to moderate and simmer the soup until the kale is tender, about 10 minutes. Season the soup with salt and pepper and serve, or let cool and freeze.