Peel and finely dice the onions and garlic. Peel the skin from the chorizo and dice the sausage. Peel, wash and chop the potatoes.
Heat the oil in a large pot. Brown the onions, garlic and chorizo in it. Add potatoes and 2 1⁄4 l water, bring to the boil. Stir in broth and simmer covered for about 15 minutes.
In the meantime wash the kale, shake dry and chop coarsely. Briefly blanch with hot water so that the cabbage does not taste bitter. Drain. Mash the potatoes coarsely with a potato masher.
Add the cabbage and continue cooking for about 20 minutes. Season to taste with salt and pepper.