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Preheat oven to 375F and line a 10”x15” jelly roll sheet or quarter sheet pan with parchment paper. Cut the paper so it has an extra inch on the sides, you’ll use this excess paper to pull the cake out of the pan after baking.
Sift the flour, salt, spices, and baking powder into a medium bowl then whisk together and set aside.
Combine eggs, vanilla, and granulated sugar in a large bowl then whisk or beat until lighter in color and smooth.
Add the grated carrots and mix until incorporated.
Pour the dry mixture into the wet then fold in until just combined.
Transfer the batter into your prepared baking sheet and use a spatula or offset spatula to smooth out. The batter will be quite thin after it’s smoothed out but that’s as it should be. Bake for 13-15 minutes at 375F. The cake is done when the center springs back when pressed lightly.
While the cake bakes prepare your thin kitchen towel by dusting it with powdered sugar. When the cake is done lift it out of the pan and invert onto the sugared cloth.
Peel back the parchment paper and roll tightly then place the rolled cake on a wire rack to cool completely.
Make the cream cheese frosting by creaming the butter and cream cheese in a stand mixer fitted with a whisk attachment or large bowl if using a hand mixer. Add the vanilla and powdered sugar then beat until fluffy, smooth, and light in color. Reserve about ¼ cup of frosting for the buttercream carrots.
Unroll the cake on your counter then spread the frosting leaving about half an inch unfrosted on the two long sides as well as the short side that will be on the outside after rolling.
Roll the cake back up then wrap in plastic and refrigerate for at least an hour so the frosting can set up.
Divide the reserved buttercream into two batches, color one green and the other orange then transfer to piping bags and snip the tips off.
Once the cake is chilled, dust with powdered sugar and pipe little carrots on the top and sides using the orange and green frostings (see notes for decorating tips).
Cut into slices using a sharp serrated knife and enjoy!