Preheat the oven to 325°F. Line a muffin tin with cupcake wrappers.
In the bowl of a stand mixer fitted with the paddle attachment, beat together the eggs, sugar and vegetable oil.
In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, allspice and salt. Gradually add the flour mixture to the stand mixer, beating just until combined then stir in the carrots.
Fill the cupcake wrappers 2/3 full with the batter then bake the cupcakes for 20 to 25 minutes or until a toothpick inserted comes out clean. Remove the cupcakes from the oven and transfer them to a rack to cool completely while you make the frosting and decorations.