Preheat oven to 375 degrees F. Grease a jelly-roll pan (15x10x1-inch) and line with parchment paper. Set aside.

Combine carrot, pineapple, and walnuts in a medium bowl. Set aside. Mix together flour, baking powder, baking soda, spices, and salt in a large mixing bowl. Mix together buttermilk, molasses, eggs, oil, and dark brown sugar in a separate medium bowl.

Now add the buttermilk mixture to the flour mixture and stir with a wooden spoon to make a batter, then fold in the carrot mixture. Pour into the prepared pan and bake in the preheated oven for 25 to 30 minutes, until cake is set and springs back when gently pressed in the middle. Remove the pan from the oven and allow cake to cool on a rack while you prepare the cream cheese frosting and cointreau carrots.

Once the cake has cooled, carefully remove cake from pan. Cut into three equal-size rectangles by cutting the cake crosswise twice. Stack the cake into three tiers with cream cheese frosting in between each layer. Frost the outside of the entire finished cake, smoothing off the edges and corners (an offset spatula works well). Top with cointreau carrots and drizzle a little of their syrup on top.

Using a standing mixer, beat cream cheese and butter in a large mixing bowl until it is blended and has a smooth, light texture. Add the powdered sugar, vanilla, and lemon zest and beat until combined. Continue to beat until smooth and glossy, about 7 minutes.

Slice carrot into thin rounds. Put carrot, butter, sugar, cointreau, and salt in a small saucepan and place over medium heat. Bring to a simmer and reduce until carrots are tender and mixture is syrupy, about 5 minutes.