Add flour, baking powder, cinnamon, ginger, nutmeg, and cloves in a sifter sitting over a bowl. Sift the ingredients until blended. Set aside.
Add eggs in a large mixing bowl. Beat with an electric mixer set on high until the eggs are thick and frothy. (5 minutes)
Continue beating on high while adding in the vanilla and sugar. Beat for 1 minute.
Slowly fold in the dry ingredients, stirring to combine. Fold in the carrots.
Dump the batter onto the prepared cookie sheet. Use a rubber spatula to spread the batter on the cookie sheet.
Make sure that you spread it to all four corners of the cookie sheet. Bake at 350 degrees for 10-12 minutes. (Insert a toothpick in the center of the cake to make sure the cake is done.)
Lay a clean kitchen towel on the countertop. Sprinkle 1/2 cup powdered sugar on the kitchen towel.
As soon as the cake comes out of the oven, flip the cake onto the towel.
Carefully peel the parchment paper off of the cake. Fold one end of the towel over a short end of the cake.
Start at the short end of the cake and roll the cake into the towel. Set the cake aside to cool to room temperature. (1 hour)