Cut a small cross in the bottom of the tomatoes and place them in a bowl. Bring enough water to cover the tomatoes completely to a boil. Pour the boiling water over the tomatoes and let them sit for one minute then drain them, cool slightly and peel.
Cut the peppers in half lengthwise and remove the seeds and pith. Cut the peeled tomatoes into quarters.
Rub the peppers all over with olive oil and place them cut side up in rimmed oven proof dish.
Stuff two tomato quarters into each pepper. Sprinkle with chopped garlic and anchovies. Tear or cut the basil and place leaves on top of the tomatoes. Drizzle with olive oil and add pepper to taste. (If you are not using anchovies, you may want to salt them as well)
Place on the top rack of the oven and roast for 30-40 minutes until the edges of the peppers have started to char. Let cool slightly and carefully remove to plates as desired. The tomatoes will have released their juices filling the peppers.