“This vertical spin on a cherished classic is packed with spices and sure to impress. The brown butter cream cheese frosting truly takes the vertical cake over the top!” —Mark Neufang, Milwaukee, Wisconsin
Preheat oven to 350°. Line 2 greased 15x10x1-in. baking pans with parchment; grease paper. Set aside. Sift flour, ground ginger, cinnamon, salt, nutmeg and cloves together twice. Place pecans in a food processor; pulse until finely ground. Transfer to a bowl; toss with carrots, fresh ginger and zest.
In a large bowl, beat egg yolks until slightly thickened. Gradually add 2/3 cup sugar, beating on high speed until thick and lemon-colored. Fold in flour mixture, then carrot mixture.
Place egg whites in another large bowl. With clean beaters, beat egg whites on medium until soft peaks form. Gradually add remaining sugar, 1 tablespoon at a time, beating on high after each addition until sugar is dissolved. Continue beating until stiff glossy peaks form. Fold a fourth of the whites into batter, then fold in remaining whites. Transfer to prepared pans, spreading evenly.
Bake until golden brown and top springs back when lightly touched, 18-22 minutes. Cool 5 minutes. Invert cakes onto tea towels dusted with confectioners’ sugar. Gently peel off paper; trim ends. Roll up cakes in towels jelly-roll style, starting with a short side. Cool completely on a wire rack.
For the frosting, place 1 cup butter in a small heavy saucepan; melt over medium heat. Heat until golden brown, 5-7 minutes, stirring constantly. Remove from heat. Cool until thick and creamy, but not hard, stirring occasionally.
Meanwhile, in a heatproof bowl of stand mixer, whisk egg whites, 1 cup sugar and salt until blended. Place over simmering water in a large saucepan over medium heat. Whisking constantly, heat mixture until a thermometer reads 160°, 8-10 minutes. Remove from heat. With whisk attachment of stand mixer, beat on high speed until cooled to 90°, about 7 minutes. Using the paddle attachment, gradually beat in remaining 1/2 cup butter, a few tablespoons at a time, on medium speed until smooth. Beat in vanilla and cooled browned butter until smooth; transfer to another bowl. Add cream cheese to mixer bowl, beat until smooth. Gradually add buttercream back to bowl; beat until combined.
Unroll cakes; cut each into two 15x5-in. strips. Spread 1 cup frosting on each strip to within 1/2-in. of edges. Refrigerate until frosting is firm, at least 20 minutes.
To assemble cake, tightly roll up 1 strip jelly-roll style, starting with a short side, lifting slightly as you roll. Carefully align seam of roll with short side of another strip. Continue to roll, jelly-roll style, adding remaining strips; seal seam. Carefully stand rolled cake on its end on a serving platter. Spread remaining frosting over top and sides of cake. Refrigerate at least 2 hours or overnight. Let stand at room temperature 15 minutes before slicing.