Preheat the oven to 180C/350F/gas mark 4. Heat an ovenproof stainless steel frying pan over a good heat and add the olive oil. Lightly season the fish and add to the pan, skin side down, if applicable.
Add the sliced chorizo and bay to the pan and cook quickly alongside the fish to allow the flavours of the chorizo to be released. When the fish skin is lightly coloured, turn the fillets over to colour the flesh side, then turn back to the skin side. Transfer the pan to the oven to finish cooking the fish. Exact cooking times are difficult to predict, as it depends on the thickness of the fish, but about five minutes in the oven should be about right for the average fillet. Add time for thicker fish and reduce the time for thinner fish – or do not place in the oven at all. The fish should be cooked so that the skin is lovely and crisp and caramelised and the inside firm but not rubbery. It’s not essential to finish off the fish in the oven, but for a thick fillet the more ambient heat of the oven cooks the middle well without burning the outside.
While the fish is cooking, melt the butter in a medium saucepan and add the cream. You can decide how much or how little cream you prefer in your mashed potato. A little splash is usually enough to gain a lovely silky smoothness. Add the mashed potato to the pan with a little seasoning, and work the butter and cream into the potato as it heats up. A heatproof spatula is good for this. Add the olives and parsley to the hot potato and stir in.
Add the basil leaves to the fish pan then transfer the fish, chorizo, bay and basil to a warm plate to rest. The fat in the frying pan will be a combination of olive oil and chorizo fat, flavoured by the fish. Tip two-thirds of this fat over the fish then add the well-drained green beans to the hot pan. Return the pan to the heat and toss the beans into the hot oil for a minute to heat through and flavour them. Don’t leave too much oil in the pan – they just need enough for a minute’s cooking and a gentle roll about in the flavour.
Set a scoop of olive mash in the centre of four hot plates, and then spoon a portion of beans on to each one. Place a piece of fish onto the beans and sprinkle the cooked chorizo sausage and basil around. Spoon some of the cooking juices and oil over the fish and serve.