Make the boats by cutting 4-6 circles out with a pastry cutter. Place some baking beans wrapped up in parchment paper into the centre of each pastry circle – this will prevent the middle of the pastry from puffing up and will form a bowl shape. Cook the puff pastry in a 200C preheated oven on a baking tray.
Cut the peppers into quarters, discarding the stalk and seeds. Place under a hot grill until the skin blisters and blackens. Remove from the heat and allow to cool. Peel or rub off the skins and finely dice peppers.
Drain the can of artichokes and chop into similar size dice to the peppers. Place both in a container with the olive oil, season with salt and pepper and cover. This may be left overnight in the fridge.
To serve, drain the peppers and artichokes of the oil and stir in the basil leaves. Arrange the pastry boats on a platter and place a teaspoonful of the mixture into each one.