Time to cook the fish – hot and fast. On a high heat, melt 1 1/2 ounces butter in a non-stick skillet large enough to hold the fillets in a single layer.
As soon as the butter starts to foam, add all the fillets, skin side down. Turn the heat to medium-high and let the fillets sizzle away for two minutes. Then turn them and cook for another two minutes.
Turn off the heat and add the lime juice all over the fillets. Leave them to cool in the skillet for 30 minutes.
Once the mashed potatoes are cold, transfer them to a mixing bowl and add the chilies, chorizo, cilantro, anchovies, and black pepper. Stir until all the ingredients are combined.
Transfer the fillets – and all their juices – from the skillet onto a board and roughly chop them, making sure the skin and juices get mixed in with the flesh.
Add the fish to the mixing bowl and stir gently so that you get an even mixture that still keeps some body in the fish.
Using your hands, form the mix into eight round patties, about 3 inches in diameter and 2/3 inch thick. Time now for coating them.
Line up three side plates on your work surface, plus a plate large enough to hold the patties in a single layer.
Add the flour to the first side plate, the beaten egg to the middle one, and then a thorough mix of parmesan and bread crumbs to the last side plate.
Begin by coating the first patty in flour, then give it a light coating of the egg, and finally a generous coating of the parmesan and breadcrumb mix. Place the coated cake onto the large plate.
Repeat the process until you have eight coated fishcakes. Put the large plate with the fishcakes in the refrigerator for 30 minutes – good time now to make the salsa.