Preheat the oven to 350F/180C.
Trim but do not completely discard the stems on each of the eggplants. Using a sharp paring knife, Make a slit down the middle, lengthwise, of each eggplant, careful not to cut through to the bottom or split the eggplant in two.
Pour 3 tablespoons olive oil in a skillet large enough to hold the eggplants snuggly in one layer. Place the eggplants in the skillet over the olive oil. Cover and cook on low heat, turning the eggplants on occasion with kitchen tongs, to keep them from browning too much. Cook for a total of about 15 minutes, until softened and lightly colored.
In the meantime, place the remaining olive oil in a deep skillet and heat over low flame. Add the onions and a pinch of salt. Cook slowly, over low heat, for about a half hour, until golden but not caramelized. Stir in the garlic. Add the grape molasses or wine and continue to cook another 5 – 6 minutes, until golden brown. The onions should be soft, not overcooked and shriveled.
Remove, season to taste with salt and pepper, and stir in the parsley. Let cool.
Oil a shallow, medium-size ovenproof baking dish and spread 3 – 4 tablespoons of the tomato puree or sauce over the surface.
Place the eggplants snuggly in the baking dish, slit side up. Season lightly with salt and pepper. Fill with the onion mixture. Spoon a little more tomato on top. Cover with a piece of parchment and seal with aluminum foil and bake for 30 – 40 minutes, until everything is beautifully melded together. Remove, cool, and serve.