Put a 12-inch skillet with a lid over medium heat and let it warm for about 1 minute.

Brown the chorizo: Add the chorizo to the skillet. Break it into small pieces with a wooden spoon and cook for 5 to 6 minutes, until it is browned and no longer pink.

Use a slotted spoon to transfer the cooked chorizo to a plate. Leave about 2 tablespoons of fat in the skillet.

If the skillet looks dry, add the olive oil. Keep the skillet over medium heat.

Start the potatoes: Add the potatoes to the skillet and spread them into an even layer. Sprinkle with 1/2 teaspoon of the salt.

Cook the potatoes for 8 minutes, stirring every 2 to 3 minutes, until they have browned edges and are starting to soften.

Pour 1/4 cup water into the skillet. Cover with the lid and cook for 4 to 5 minutes, until the potatoes are almost tender when pierced with the tip of a knife.

Uncover the skillet. Add the onion and cook for 3 minutes, stirring often, until it starts to soften.

Add the cabbage to the skillet. Sprinkle in the remaining 1/2 teaspoon salt and the black pepper.

Stir the cabbage into the potatoes and onion until it starts to wilt. Cover the skillet again and cook for 4 minutes.

Uncover the skillet and stir. Cook for 2 to 3 minutes more, until the cabbage is tender and most of the moisture in the pan has cooked away.

Return the chorizo and any juices from the plate to the skillet. Stir everything together and spread the mixture into a mostly even layer.