Preheat oven to 350 degrees. Butter a 9x2 inch square baking pan and line with parchment paper. Set aside.
In the bowl of a food processor, pulse together butter and brown sugar until pale and fluffy. Add egg yolks, one at a time, pulsing after each addition. Add orange zest and juice; pulse to combine. Add cinnamon, cloves, nutmeg, and ginger; pulse until mixture is well combined.
In a large bowl whisk egg whites with a pinch of salt until stiff. Gently fold in almonds, walnuts, flour and carrots; fold cake mixture into egg white mixture. Pour batter into prepared pan and bake until golden and a toothpick inserted into the center comes out clean, about 1 hour. Let cake cool in the pan 10 minutes before turning out onto a wire rack to cool.
In a medium bowl, mix together mascarpone, cream cheese, confectioners sugar, and lime zest and juice. Spread mixture over top of cooled cake and sprinkle with chopped walnuts.