Step 1Heat the oven to 350 degrees. Grease 2 (8-inch) baking pans and line the bottoms of the pans with parchment paper. Grease the parchment paper and set the pans aside.
Step 2In the bowl of a stand mixer with the whisk attachment, or in a large bowl using a hand-held mixer, whip the eggs and 1 cup sugar until the mixture is thick and light (ribbon stage), about 5 minutes.
Step 3With the mixer running, pour in the oil to incorporate and continue whipping until the mixture is light and fluffy, about 5 minutes.
Step 4In a separate large bowl, whisk together the flour, cinnamon, baking soda, baking powder, salt and the remaining 1 cup sugar.
Step 5Using a whisk, add half of the egg mixture to the dry ingredients, gently whisking just to combine. Add the remaining egg mixture and whisk just to combine. Be careful not to overmix or the cake will not rise properly. Gently fold the carrots and currants into the batter with a spatula just until incorporated.
Step 6Divide the batter evenly between the two pans. Bake the cakes on the same rack in the center of the oven just until set, 30 to 40 minutes, rotating halfway through for even cooking. A toothpick inserted will come out clean when the cakes are done. Remove the pans to a rack until cool before unmolding. While the cakes are cooling, make the cream cheese frosting.
Step 1In the bowl of a stand mixer with the paddle attachment, or in a large bowl using a hand-held mixer, cream the butter until light and smooth, 3 to 5 minutes.
Step 2Add the cream cheese and continue mixing until smooth. Scrape the sides of the bowl often to make sure the contents are completely combined.
Step 3Mix in the powdered sugar and vanilla if using. Add the sugar in three stages, mixing and scraping the sides of the bowl with each addition until the frosting is smooth.
Step 4Frost the cake then chill slightly to allow the frosting to thicken before serving.