Heat the barbecue grill plate to medium and fry pineapple rings and ham until golden brown on both sides.
Heat the barbecue flat plate to a medium/high heat and add the olive oil and butter. Once butter has melted, crack the eggs on to the flat plate and fry until tops of whites are set but the yolks are still runny.
Cut Brioche buns in half and smear with tomato relish or aioli. Add the pineapple ring, ham and fried egg. Season with salt and pepper and garnish with fresh flat-leaf parsley.