For the roast brill, heat the oil and butter in a frying pan. Season the fish and fry until golden-brown on both sides, about 3-4 minutes. Transfer to the oven to cook for about five minutes.
For the tapenade, place all the ingredients into a food processor and blend until smooth.
For the potatoes and olives, heat the oil and butter in a frying pan and fry the potato quarters until they start to take on some colour. Stir through the olives and seasoning, and continue to cook until the potatoes are nicely browned.
To serve, arrange the fish on a bed of the potatoes and olives, and spoon the tapenade over the top. Garnish with the cherry tomatoes and wedges of lemon.