Preheat an oven to 425°F. Line cupcake pan with paper liners.
In a large bowl, stir together the flour, baking powder, baking soda, salt and spices.
In another bowl, whisk together the eggs and brown sugar until blended. Whisk in the buttermilk and butter.
Add the egg mixture to the flour mixture and, using a rubber spatula, stir just until evenly incorporated. Do not over-mix.
Fold in the carrots just until evenly distributed.
Spoon the batter into the prepared cupcake pan, filling them 1/3 of the way full.
Remove the cream cheese frosting log from freezer and divide/slice into 12 equal parts.
Place a piece of the frozen cream cheese frosting on top of and in the middle of the cupcake batter.
Top each cupcake with another 1/3 of the batter, right on top of the cream cheese frosting piece.
Bake until the cupcakes are golden brown, 15 to 18 minutes.
Transfer the pan to a wire rack and let cool for 2 minutes, then turn the cupcakes out onto the rack.
Let cool and serve.