Preheat the oven to 190C/375F/Gas 5.
Pour boiling water over the plum tomatoes, leave for 10 seconds, carefully remove from the water and refresh in a bowl of cold water. Peel off the tomato skins.
Place the halved peppers into an ovenproof dish (preferably one that will be nice enough to present later), cut-side up.
Place the garlic inside the peppers and then fit the tomatoes inside too, pushing them gently into the space. Add a small pinch of salt and a grinding of freshly ground black pepper. Spoon over the olive oil and then place into the oven. Bake for about 45 minutes to one hour, turning the heat down a little if you notice any excessive scorching of the peppers.
Once they are nicely softened and have slightly collapsed, remove the peppers from the oven. Criss-cross each pepper half with an anchovy, baste with the oily juices and allow to cool to room temperature.
Top with basil leaves and serve.