To make cake: Position rack in the bottom third of oven; preheat oven 350. Butter and flour 9x13 heavy-duty cake pan. Soak currants in 1/2 cup hot tap water; 15 minutes. Drain, set aside.
In processor, chop carrots very fine. Transfer to a small bowl and rinse processor bowl.
In a large bowl, combine flour, baking soda, salt and spices. Whisk to blend thoroughly. Transfer 1/4 cup of this mixture to a small bowl an add drained currants and nuts. Toss to combine.
In processor, mix eggs and both sugars until well blended. While running, slowly add oils in a steady stream until combined. Scrape mixture into flour mixture. Stir to combine. Add carrots and currant-nut mixture; stir to combine.
Scrape the batter into prepared pan. Bake until toothpick inserted in center comes out clean; 50 minutes. Let cool on wire rack to room temperature before inverting pan to remove cake. Let cool completely before frosting.
To make frosting: Beat butter on medium until quite light, fluffy and resembles whipped cream, about 3 minutes. Add cream cheese one piece at a time, beating well after each addition. When all the cream cheese is incorporated, reduce speed to med-lo and gradually add sugar and vanilla. Mix just enough to remove any lumps; scrape the bowl as needed. If the frosting seems a bit loose; refrigerate for a few minutes.
To frost the cake: Scrape 2/3's of the frosting onto the center of the cake. With a narrow off-set spatula, push the frosting from the center out to and just over the cake's edges. Spread with a few strokes as possible to prevent crumbs from catching in the frosting. Cover the top of the cake first then use the remaining frosting along with what is over the edge to cover the sides. Sprinkle nut on top of the cake and press into the sides.