For the cake layers: Preheat the oven to 350 degrees F. Grease and line the bottoms of three 8-inch cake pans with cooking spray and parchment and set aside.
Sift together the flour and baking powder in a large bowl, then lightly stir in the salt and set aside.
Cream together the butter, coconut oil and granulated sugar in a stand mixer fitted with the paddle attachment on medium-high speed until light and fluffy, 3 to 4 minutes. Add the eggs, one at a time, beating well after each. Reduce the mixer to low and add the vanilla and sour cream. Gradually add the dry mixture and mix until about 80 percent combined. Divide the batter evenly among 3 bowls. In the first bowl, stir in the carrot juice and 1/4 cup milk and fold together until smooth and just combined. In the second bowl, add the beet juice and 1/4 cup milk and fold together until smooth and just combined. Blend together the mint leaves and remaining 1/2 cup milk in a blender until very smooth, scraping the sides as needed. Add this to the third bowl and fold together until smooth and just combined. Transfer the batters to the cake pans and spread them out evenly.
Bake until the tops of the cakes are thinking about starting to turn brown and a toothpick inserted in the centers comes out with a few crumbs on it; begin checking for doneness at 30 minutes and try your darnedest not to let it overbake. Let sit in the pans for 10 minutes, then transfer to a wire rack to cool completely.
For the buttercream frosting: Beat together the butter and cream cheese in a stand mixer fitted with a paddle attachment until creamy. Gradually add the powdered sugar, then mix in the salt, vanilla and heavy cream. Mix until creamy.
Level the tops of the cake layers, retaining the scraps, then stack them up with a layer of frosting in between each. Frost all over and decorate as desired.
To make a mini cake, stack up the cake scraps that were cut off from the layers and cut out four 2 1/2-inch circles. Stack them on top of each other and frost all over. (The scraps should be moist enough that they'll all stick together!)
Use food coloring to dye the marzipan (deep purple for beets and orange for carrots). Mold into vegetables, using rosemary for the stems. Place on top of the cake.