Cut a slice across the top of each tomato, leaving a piece attached to serve as a hinge for the “top”. Hollow out the tomatoes and turn upside down on plate to drain for about one hour.
Soak currants in tepid water for 15 minutes; drain well.
Heat 3 tablespoons of olive oil in a medium skillet over medium heat. Add onion and cook until translucent, about 5 minutes. Add the rice and cook, stirring frequently, about 5 minutes more. Add currants, cinnamon, allspice, pepper, salt and sugar and stir. Add water.  Reduce heat to low, cover and cook until water is absorbed, about 20 minutes. Remove from heat and cool. Stir in pine nuts, mint and dill.
Preheat oven to 425 degrees. Arrange tomatoes upright in a greased baking dish and sprinkle with remaining 1 tablespoon of olive oil and a pinch each of sugar and salt. Bake, uncovered, for about 10 minutes; tomatoes will look as though they are about to collapse.  Remove from oven and cool.
Stuff tomatoes with rice mixture and serve at room temperature, garnished with fresh mint leaves. Serves 4.