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Preheat oven to 375°F. Line 15x10x1-inch baking pan with parchment paper, extending paper 1-inch past ends of pan to use as handles. Sift flour, spices, baking powder and salt into a medium bowl; set aside. Beat eggs, sugar and vanilla in large bowl with electric mixer on high speed about 5 minutes or until very thick and pale in color, scraping sides of bowl occasionally. Stir in carrots and oil. Gradually add flour mixture, stirring just until blended. Spread batter evenly in prepared pan.
Bake 13 to 15 minutes or until toothpick inserted in center comes out clean and center springs back when pressed lightly.
Place clean kitchen towel on work surface; dust with 2 tablespoons confectioners' sugar. Loosen cake around sides of pan with small knife. Turn out onto sugared towel, parchment paper-side up. Fold 1 side of towel over short side of cake, then roll up cake jelly-roll style. Cool cake completely on wire rack.
For the Frosting, beat cream cheese, butter and extracts in large bowl with electric mixer on medium speed until well blended. Gradually add confectioners’ sugar, beating well after each addition, until smooth. Reserve 1/4 cup frosting; set aside for decorating.
Unroll cake onto towel. Peel off parchment. Spread remaining cream cheese frosting evenly over cake, leaving a 1/2-inch border unfrosted. Using towel, roll up cake and place seam-side down on large sheet of plastic wrap. Wrap cake firmly to keep shape. Refrigerate 1 hour to allow frosting to set.
Divide reserved frosting evenly into two separate small bowls. Tint one bowl green (1 drop Green Food Color) and one bowl orange (1 drop Red + 2 drops Yellow Food Color). Transfer tinted frosting to piping bags fitting with medium round tip. Remove cake from plastic wrap and place seam-side down on serving platter. Dust cake with confectioners’ sugar and pipe carrot shapes on top and sides, as desired, using tinted frosting.
Decorating Tip: To pipe the icing carrots, start with the thick top of the carrot and finish with the pointy part. Squeeze a bit more at first, then release and pull the tip away after you’ve stopped squeezing the piping bag. Then pipe little green leaves on top of the carrot, using a small leaf tip, if desired, or simply snip the tip off your piping bag and decorate away!