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Preheat oven to 350F. Line a 10x15 inch jelly roll pan (or cookie sheet with a raised edge) with parchment paper. Allow the parchment paper to come at least 1 inch above the sides of the pan for easy lifting the finished cake from the pan. Spray the parchment paper in the pan with non-stick cooking spray.
In a medium mixing bowl, whisk together the flour, baking powder, cinnamon, ginger, nutmeg, and cloves; set aside.
In a large mixing bowl or the bowl of a stand mixer, beat the eggs at high speed for 5 minutes until thickened and frothy. Add the sugar and vanilla, then beat at high speed for 1 minute.
Pour the dry mixture into the wet mixture and stir gently just until combined. Stir in the grated carrots.
Spread the cake batter evenly into the prepared jelly roll pan, spreading all the way to the edges. Bake at 350 for 10-12 minutes until a toothpick inserted into the center comes out clean (do not under bake).
Sprinkle a large, clean kitchen towel very generously with powdered sugar (use at least ½ cup). As soon as the cake comes out of the oven, turn the cake out of the pan onto the prepared towel. Peel away the parchment paper carefully.
Fold the end of the towel over one of the short ends of the cake. Roll the cake up into the towel, starting at the short end. Set the cake aside to cool completely to room temperature, about 1 hour.
While the cake is cooling, prepare the frosting. In a large mixing bowl, beat together the cream cheese and butter with an electric mixer until smooth. Add the vanilla extract and powdered sugar and mix on low speed until combined and the frosting is creamy.
Very gently, unroll the cooled cake roll and be sure it is fully released from the towel. Spread the frosting onto the cake, edge to edge. Re-roll the cake gently. Transfer the cake roll to a plate, seam side down.
Chill the cake roll in the refrigerator for 30 minutes. Dust with powdered sugar before serving.