Preheat oven to 350 degrees. Coat a large baking sheet with nonstick vegetable spray.
In a large bowl, whisk eggs and sugar until thick and pale, about 3 minutes. Stir in oil. Fold in flour. Refrigerate for 1 hour.
Divide dough into 3 pieces. On a floured board, press 1 piece of dough into a rectangle about 6 by 10 inches. Spread 2 tablespoons preserves over the dough. Sprinkle on 1/3 cup raisins, 1/4 cup currants, and 2 tablespoons nuts. Dust lightly with cinnamon. Roll up as for a jelly roll. Place on prepared baking sheet. Repeat with remaining ingredients.
Bake in preheated oven 35 minutes. Let cool. Cut into slices 1/2-inch thick.