Roasting eggplants directly over an open flame intensifies their flavor.
Place each eggplant directly on stove burners over medium to medium-high flame. Cook, turning frequently, until the skin is lightly charred and inside flesh is very soft, about 20 to 30 minutes. Remove from burners; set aside on a large baking pan until cool enough to handle.
Cut eggplants in half and remove seeds (don't worry if you miss a few). Scrape flesh from skins using a table knife; transfer flesh to a food processor. Add 2 tablespoons lemon juice, 3 tablespoons olive oil, 3 teaspoons salt, 1/4 teaspoon pepper, and 1 teaspoon garlic. Pulse about 25 times to combine, but not puree, the mixture. This can be made up to 2 days in advance and refrigerated until ready to use.
Heat oven to 400 degrees. Heat remaining 1 teaspoon oil in a large skillet over medium- high heat; add tomatoes, remaining 1 teaspoon garlic, sugar, vinegar, remaining 1/2 teaspoon salt and 1/8 teaspoon pepper. Cook until tomato skins just start to blister, about 2 minutes. Add wine; cook until liquid thickens and tomatoes are soft, about 7 minutes. Stir in chopped oregano.
If eggplant has been refrigerated, return to room temperature. Transfer to a serving bowl; arrange tomatoes around edge. Garnish with oregano leaves, if desired.
Cut each pita into 2 flat circles; rub with lemon and season with salt and pepper. Cut each pita half into 6 wedges and arrange in a single layer on a baking sheet. Bake for 3 to 4 minutes, until golden brown on edges. Serve with eggplant dip.