Peel the potatoes and cut into cubes. Clean the soup greens and dice. Press on the garlic clove. Wash the vegetable leaves, cut into strips.
Heat the oil in a saucepan, add the soup greens and garlic clove, sweat for about 5 minutes. Add the potato cubes and sweat them too. Deglaze with water or stock, add about 2/3 of the leaves, season with salt and pepper. Bring to the boil and simmer for about 15 minutes. Fish out the garlic cloves. Mash a large part of the potatoes in the pot with a potato masher, there should be larger pieces left. If necessary, add water or stock if the soup is too thick. Add the remaining leaves and simmer for about 5 minutes.
Let the chorizo and black pudding slices warm up in the soup before serving.
Drizzle a little good olive oil on each plate of soup according to taste, some sherry or balsamic vinegar also goes well.