Put the chorizo in a large heavy pot with a lid over high heat. Cook until the fat is rendered and the meat has browned, about 10 minutes. Remove the meat with a slotted spoon to a plate and reserve. Add the onions to the pot with a pinch of salt and pepper and cook until softened, 6 to 8 minutes. Add the chorizo back to the pan and drop in the mussels. Pour in the wine, cover, and bring to a boil. Cook until mussels have opened, about 4 to 5 minutes.

Remove the lid and discard any mussels that have not opened. Stir very well until the mussels are coated in the wine and onions. Transfer to a serving dish, garnish with the parsley and serve immediately.