Line 18 regular-size muffin tins with cupcake paper liners.
In a large bowl, mix together the carrot, eggs, sugar, vegetable oil, buttermilk, and vanilla.
In another bowl, mix together the flour, baking soda, baking powder, cinnamon, ginger, cloves, and salt.
Mix the flour mixture in with the carrot mixture until well mixed.
Pour batter into lined cups. Martha recommends filling the cup about 2/3 cup full. I like to live dangerously and go for a little over 3/4 full – usually a 1/3 cup measuring cup gets me close.
Bake for 23 to 28 minutes. They’re done when the top springs back when you tap it, or a when a cupcake tester or toothpick comes out clean.
Cool on wire racks for about 10 minutes, then pull the cupcakes out of the tins and let them cool on the racks completely before frosting.
Make the frosting. On medium speed, beat together the butter and cream cheese until fluffy.
Reduce speed to low and add the powdered sugar, 1/2 cup at a time. I really advise against more than that, because you may find yourself disappearing in a powdered sugar cloud. Not that I’d know, not at all.
And finally mix in the vanilla.
And, frost your cupcakes! I topped mine with a little Demerara sugar for a little extra sparkle.