Preheat oven to 400°F. Mist a large roasting pan with Olive Oil.
Remove leaves from eggplants, but leave the stems on. Cut the eggplants in half lengthwise, through the stem. Using a small sharp knife, make a deep slit lengthwise down the flesh side of each eggplant half: start about 1 inch below the stem and stop about 1 inch from the bottom. Do not cut completely through the skin.
Brush the eggplant all over with 2 tablespoons Olive Oil. Sprinkle the eggplant flesh with 1/4 teaspoon salt. Place cut-side down in the prepared roasting pan. Bake for 15 minutes.
Meanwhile, quarter and thinly slice onion. Finely chop garlic. Thinly slice 1 bell pepper quarter and set aside; dice the remaining pepper.
Cut 1 tomato into 4 wedges and set aside; dice the remaining 2 tomatoes.
Heat 1 tablespoon Olive Oil in a large nonstick skillet over medium-high heat. Add onion and garlic; cook, stirring, for 1 minute. Add the diced bell pepper, the diced tomatoes, 1/2 cup parsley, sugar, bay leaves and the remaining 3/4 teaspoon salt. Cook, stirring, for 3 minutes.
Remove from heat; discard bay leaves.
After the eggplant has baked for 15 minutes, remove from the oven. Carefully turn each eggplant half over and use 2 spoons to open and widen the slits. Stuff the slits with the vegetable mixture, pressing it down gently. Place a wedge of tomato in the middle of each half; evenly divide the reserved sliced pepper among the halves.
Add 1/4 inch hot water to the roasting pan. Drizzle the eggplant with the remaining 2 teaspoons Olive Oil. Bake 30 minutes more.
Let cool for at least 15 minutes. Serve warm or cool completely, refrigerate and serve cold. Garnish with the remaining 3 tablespoons parsley and lemon wedges.