Cut unpeeled eggplants into 1/2" diagonal slices, spread slices onto a cutting board, sprinkle with salt & press with a plate to get rid of excess liquid. Allow to drain for 30 minutes. Wipe with a damp cloth.
Heat enough olive oil to cover bottom of a large skillet. Fry gently over medium heat, turning often till tender. Remove from pan & drain. Plunge tomatoes into boiling water for a few seconds, peel & deseed. Saute remaining pulp in a little olive oil till soft. Add garlic & parsley. Cover, reduce heat & cook for 30 to 40 minutes. Remove from heat, cool, add lemon juice, sugar, salt & pepper.
Place eggplant in a shallow serving dish or glass bowl. Pour tomato mixture on top & chill till ready to serve. Garnish with parsley sprigs.