Preheat oven to 350 degrees F. Adjust rack to middle of the oven and prepare a rimmed 18" x 13" baking sheet. Grease the bottom, then line with parchment paper. Grease parchment paper.
Whisk dry ingredients in a large bowl; flour, baking powder, baking soda, spices and salt.
Whisk sugar, oil, eggs, and vanilla together until mixture is smooth. Stir in carrots and currants.
Fold in flour mixture and mix until just combined. Spread batter in prepared baking sheet. Tap the baking sheet to get out the bubbles and smooth with an offset spatula.
Bake until center of cake is firm to the touch, about 15 to 18 minutes. Cool in pan on wire rack for 5 minutes. Leave parchment on cake and invert onto wire rack. Allow to cool completely, about 30 minutes.