Preheat oven to 350°F. Line the bottom of two 8" cake pans with parchment paper.
In a large bowl, whisk together the flour, sugars, baking soda, salt, cinnamon, nutmeg, ginger, and allspice.
Add the soy milk, butter, vanilla, and apple cider vinegar. Mix until just combined.
Add the carrots and whisk briefly to incorporate - do not over mix.
Divide batter into the prepared pans.
Bake for 35-40 minutes, until the center of the cake feels firm and a toothpick comes out clean. Let cool completely on a wire rack. For best results, refrigerate overnight after cooling.
Invert the first cake onto a plate or cake stand. Add a layer of frosting, then add the other cake.
Use an offset spatula to spread a very thin layer of frosting all over the cake. This is a crumb coat. This covers the cake in frosting, allowing for a smoother final coat. Refrigerate for 1-2 hours to set the frosting.If you do not want to crumb coat, feel free to just frost the entire cake at this step.
If desired, mix a few tablespoons of frosting with matcha powder to create a green color. And mix a quarter cup of frosting with turmeric to create an orange color.
After the cake is chilled again, use an offset spatula to cover the cake with the remaining frosting. Use a plastic bag with a small hole cut in the corner or a piping bag to draw a few carrots on top of the cake.Serve! Keep any leftovers refrigerated.