Carefully separate the grape leaves, place in a large bowl and pour boiling water over them to cover. Let the leaves soak for 20 minutes, then drain and rinse to remove excess salt. Drain the leaves, snip off the stems (reserving stems), and lay the leaves on a towel to dry.
In a large saucepan, heat 3/4 cup olive oil, add the onions, salt and pepper, and cook over medium heat until onions are translucent, about 10 to 12 minutes. Add the water and stir in the rice. Cover, reduce the heat to low and cook rice until water is absorbed, about 17 to 20 minutes. Transfer to a large bowl, and mix in the pine nuts, lemon juice, parsley, currants, dry mint, allspice, and additional salt and pepper to taste.
Place one leaf on a flat surface, vein side up, shiny side down. Place a rounded teaspoon of filling in the center of the leaf, near the stem edge. Fold the stem end over the filling, then fold both sides toward the middle, and form into a roll. Squeeze lightly in the palm of your hand to secure the roll. Repeat process with remaining leaves and filling.
Line the bottom of a 3 quart heavy saucepan with reserved stems, trimmings and any leftover or torn grape leaves, and arrange bundles seam sides down, packing them close together in layers.
Combine the remaining 1/4 cup olive oil with 3/4 cup water, and pour over the stuffed grape leaves. Place a small, heatproof plate on top of the stuffed leaves, cover the pan and simmer over low heat for about 45 minutes to 1 hour, or until leaves are tender and most of the liquid is absorbed. Cool the rolls in the pan, covered, then chill, covered and serve cold.