Preheat the oven to 350 degrees. Lightly spray an 8x8 square pan with non-stick spray, then create a sling with parchment paper so that the paper hangs over the sides and allows for the bars to be easily removed once baked. Set aside.
In a medium sized bowl, whisk together the dry ingredients: flours, coconut sugar, cinnamon, allspice, salt, and baking soda.
In another bowl, whisk together wet ingredients: coconut oil, eggs, milk, maple syrup and vanilla extract. Fold wet ingredients into dry, mixing with a spoon until no dry pockets remain.
Now fold in carrots, raisins, and nuts. Continue to stir until well incorporated. Spread the batter in the prepared pan. Transfer to the oven and bake for 22-24 minutes. Remove from oven and let cool.
Meanwhile, make the frosting. Combine soaked and drained cashews in a food processor with coconut cream, maple syrup, lemon juice, lemon zest, vanilla, and a pinch of sea salt. Pulse until smooth and creamy. This may take several minutes, and pausing to scrape the sides of the food processor.
Once cake is cooled (about 30 minutes), spread frosting evenly over the cake. Refrigerate for at least 1 hour, or until frosting is firm. Then cut into 12-16 squares.