Prepare the filling. Soak the currants in warm water for 20 minutes, then drain and set aside.
Heat the olive oil in a large pan and sauté the pine nuts over low heat until golden. Add the onion and sauté until barely softened. Add the hot water, bring to a boil then stir in the currants, sugar, rice, salt and pepper and cook over low heat until the water is absorbed. Add the parsley and set aside to cool to room temperature.
Cut off about 1 inch from the stem side of each eggplant, and reserve the stems. Hollow out the eggplants, leaving about ¼-to-½ inch of shell—reserving the pulp. Stuff the eggplants with the rice filling and top with the stems. Spread the pulp around the bottom of a large pot, then place the eggplants on their sides on top of the pulp. Mix the hot water, olive oil and salt and pour over the eggplants. Cover with a plate to provide weight (this keeps the eggplants from getting too fluffy and bursting).
Cook, covered, over very low heat until the eggplants feel soft to the touch, about 30 to 45 minutes. Remove from the heat and allow to cool in the pot for about 1 hour. Transfer to a serving platter and decorate with the lemon slices. Serve at room temperature or slightly chilled.