Special equipment: 12 paper cupcake liners, 3 pastry bags or resealable plastic bags, a no.16 Ateco fluted tip, a no.4 Ateco straight tip and a no.6 Ateco straight tip
For the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with paper liners.
Combine the flour, almonds, baking powder, baking soda, salt, cinnamon, ginger and allspice in a food processor and pulse until the almonds are finely ground.
Whisk together the grated carrots, granulated sugar, oil, vanilla and eggs in a large bowl until combined. Stir in the flour mixture until just combined.
Divide the batter evenly among the prepared muffin cups. Bake until a toothpick inserted in the center of a cupcake comes out clean, 10 to 15 minutes. Transfer to a rack and let cool for 5 minutes, then remove the cupcakes from the pans to cool completely.
For the vanilla American buttercream: Combine the butter, confectioners' sugar and salt in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a handheld electric mixer) and beat on low speed until mostly incorporated. Add the vanilla, increase the speed to medium-high and beat until smooth. Adjust the consistency with milk or cream as desired. Use immediately or refrigerate in an airtight container up to 3 days. (If refrigerated, allow to come to room temperature and then beat on medium-high speed until smooth before using.)
For the chocolate frosting: Sift the confectioners' sugar and cocoa into a large bowl. In another large bowl, combine 1 cup of the sugar mixture with the butter and 1 tablespoon of the milk or cream, beating with an electric mixer until smooth. Add another cup of sugar mixture and another 1 tablespoon milk or cream, beating well. Add the remaining sugar mixture and another 1 tablespoon milk or cream and beat until the frosting is fluffy. Beat in the vanilla. Add the remaining 1 tablespoon milk or cream if needed for desired consistency.
For the assembly: Use some red food coloring to tint 1/2 cup of the vanilla American buttercream pink. Scoop the pink buttercream into a pastry bag fitted with a no.6 straight tip. Scoop the remaining white buttercream into a pastry bag fitted with a no.4 straight tip. Scoop the chocolate frosting into a pastry bag fitted with a no.15 fluted tip. (You may use resealable plastic bags in place of pastry bags.)
Using the chocolate frosting, create the fur: Pipe around the edge of each cupcake by pulling a dollop of frosting to a point over the edge of the cupcake (this is the same method used to pipe a shell). Layer the frosting as needed to cover any missing spots. Pipe a second circle of fur slightly overlapping the first, covering almost the entire cupcake.
Then create the ears: Toward the edge of each cupcake, pipe a triangle shape with the chocolate frosting, layering it so that it is higher than the fur frosting. Fill in the center of the triangle with the pink buttercream. Repeat to make a second ear. Place two candy-coated chocolates in the center of the cupcakes to create eyes. Use the chocolate frosting to fill around the eyes so that they look set into the face.
Underneath the eyes, create the cheeks: Pipe two circles with the white buttercream. Pipe a smaller circle underneath and between the cheeks for the mouth. Using the pink buttercream and centering between the cheeks and above the mouth, pipe three dots in a triangle shape to make the nose. Using the frosting of your choice, pipe two lines along the center of the face from the nose, between the eyes and between the ears.