Allow about two tomatoes per serving. Make a bed of basil leaves in the bottom of an ovenproof dish that will hold the tomatoes snugly in one layer. Peel and core the tomatoes and place them core-side down on the basil. Lightly salt and pepper. Pour in enough extra virgin olive oil to come halfway up the sides of the tomatoes. Bake for 1 1/2 hours in a preheated 350°F oven, until the tomatoes are soft and lightly caramelized and have infused the oil with their perfume. Season to taste and serve spooned over cooked and drained fresh noodles.