Split the eggplant vertically in half. With a sharp paring knife, cut out the flesh from each half, leaving a shell of skin and flesh about 1cm (1/3 inch) deep. Salt the insides of the shells and let them to rest, hollow side down, on a rack for about an hour.
Cut the eggplant flesh into small pieces. In a large skillet, sauté the garlic in abundant olive oil until they start to give off their aroma then add the eggplant cubes along with the tomatoes, seasoning with salt and pepper. Simmer gently until the eggplant is perfectly soft, stirring from time to time.
Turn off the heat and mix in the rest of the stuffing ingredients. Taste and adjust for seasoning; the stuffing should be very savory. Let cool.
Take your eggplant shells and wipe them off with paper towels. Scrape off any discolored flesh from the insides of the shells with a spoon. Rub the insides with olive oil and let them stand for a fewminutes to let the oil penetrate. Then fill each shell with your stuffing.
Place the eggplant shells on a baking or gratin pan, which you will have greased with olive oil. Drizzle more olive oil over each shell. Bake in a moderate (180C/350F) oven for about 45 minutes to a hour, or until the shells are cooked through and the stuffing is nicely browned on top. (You can raise the heat to 190C/375F towards the end if need be.)
Let cool off at least a bit before serving. In my opinion, melanzane imbottite alla napoletana are at their best served only slightly warm or at room temperature.