Preheat the oven to 350 degrees F. Grease 3 (8-inch) round cake pans and line the bottom of the pans with parchment paper. Spray the paper and pans with baking spray. Set the pans aside until ready to use.
In the bowl of an electric mixer on medium speed, beat the oil and sugars together until combined. Mix in the vanilla and add the eggs, 1 at a time, mixing well after each addition. Add the carrots and pineapple and mix until combined.
In a large bowl sift together the 2 1/2 cups flour, baking powder, baking soda, salt, cardamom and cinnamon. With the mixer speed on low, add the flour mixture to the carrot mixture alternately with the buttermilk, beginning and ending with the flour. Mix until just combined. In a small bowl, toss the pecans with the remaining 1 tablespoon of flour. Fold the pecans into the batter.
Pour the batter evenly into the prepared cake pans. Bake until a toothpick inserted in the center of the cakes comes out clean, about 35 to 45 minutes. Cool the cakes in the pans on wire racks for 15 minutes. Remove the cakes from the pans and cool completely on the racks.
While the cakes are cooling, prepare the icing. In the bowl of an electric mixer on medium speed, beat the butter and cream cheese together until well combined. Reduce the speed to low and gradually add the confectioners' sugar. Mix until combined. Add the vanilla and white chocolate. Increase the speed to medium-high and beat until smooth, about 1 to 2 minutes. Set aside 1 cup of icing for decoration. Add the heavy cream and beat until combined.
To frost the cake, arrange 1 cake layer on a cake plate. Spread the top with the cream cheese icing and top with a second and third cake layer, spreading the icing between each layer. Spread the icing on top and around the sides of the cake. Apply the almonds to the sides of the frosted cake. Fill a pastry bag, fitted with a star tip, with the reserved icing and pipe a border around the top of the cake. Cut the cake and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.