Preheat the oven to 325F.  Line a muffin tin with cupcake wrappers.

In a large bowl, beat together the eggs, sugar and oil.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, allspice and salt.

Gradually add the flour mixture to the egg mixture, beating just until combined.

Stir in the carrots.

Fill the cupcake wrappers 2/3 full with the batter.  

Bake for 20-25 minutes or until a toothpick inserted comes out clean.

Remove the cupcakes from the oven and transfer them to a rack to cool completely.

In a large bowl, beat the cream cheese until smooth, then add the butter and vanilla extract.  Beat until well combined.

Add the powdered sugar and beat until smooth and creamy.

If piping the frosting, cover with plastic wrap and refrigerate until you're ready to use it.  Chilling helps firm it up.