Add the potatoes to the pan and, if the pan looks dry, add the remaining 2 tablespoons olive oil. Season with the salt. Cook, stirring occasionally, for 10 minutes more. Add the chorizo, paprika, and chile (if using) and cook, stirring occasionally, for 2 to 3 minutes more. Raise the heat to medium-high and add the wine. Simmer until slightly reduced, about 3 minutes. Add water almost to cover and bring to a simmer, stirring occasionally to encourage the potatoes to break slightly. Cook until reduced to a thick sauce, about 15 minutes. Taste and adjust the seasoning, if necessary. Serve in shallow bowls with a glass of Rioja wine alongside.