Preheat the oven to 190C/370F/Gas 5. Heat an ovenproof frying pan until hot, add the olive oil and the barramundi fillets, skin-side down. Fry for two minutes, then turn over with a fish slice and fry for a further minute.
Place in the oven for 3-4 minutes, until just cooked. Remove from the oven and place the fish on a warm plate to rest.
Return the pan to the hob and add half of the butter. Add the shallot and curry powder and lightly fry for one minute before adding the artichokes. Stir fry for one minute, then add the white wine and simmer for two minutes.
Add the shrimps and the remaining butter and heat through. Season with salt and freshly ground black pepper, to taste, and add the chives.
For the mash, place the potatoes into a saucepan and just cover with water. Add a pinch of salt and place on the heat. Bring to the boil and simmer for 10-15 minutes until tender.
Drain and return the potatoes to the pan. Place back over the heat for 10 seconds or so to remove any excess moisture. Add the butter and milk and mash to a smooth purée. Season with salt and freshly black pepper, to taste.
To serve, place a spoonful of mash onto each of four serving plates and arrange two barramundi fillets on top of the mash. Spoon the artichoke and shrimp sauce to one side, drizzling some of the juices over the fish. Serve.