For Portuguese cabbage soup, peel potatoes, cut into coarse cubes, place in a pot and cover with plenty of water. Add salt and 4 tablespoons of olive oil and bring to a boil.
In the meantime, wash the cabbage, cut into fine strips, several times until the water that drains off is just a barely noticeable greenish color.
Boil potatoes until they fall apart. Remove from heat and blend together with the water to a creamy soup. Season to taste with salt and another 4 tablespoons olive oil.
Add cabbage and cook again for about 10 minutes, stirring occasionally, until al dente.
Serve soup in warmed cups and garnish each with a slice of chorizo and some garlic.