Fry the chorizo in a pan over medium heat until crispy. Transfer to paper towels and blot dry.
Place the cooked egg yolks in a bowl with the pimientos, olives, capers, parsley, mayonnaise, mustard, salt and pepper. Mash and stir together until smooth.
Pipe the mixture into the egg halves, top with the crispy chorizo and sprinkle with smoked paprika and parsley. Serve immediately or store them in the fridge in an airtight container (to prevent browning) until ready to serve. Can be made a day ahead.