Fry the chorizo in butter in a skillet over medium heat. Keep warm until serving.
Shred the cabbage using a food processor, mandolin or sharp knife.
Sauté cabbage with remaining butter in the same skillet over medium heat. Stir occasionally for a few minutes, until cabbage is golden brown.
Add heavy whipping cream, and bring to a light boil. Reduce heat, and let simmer until the cream is reduced. Season with salt and pepper.
Add parsley and lemon zest before serving with the fried chorizo.