In a mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In another bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

In a separate bowl, combine the grated carrots, cream cheese, powdered sugar, vanilla extract, and cinnamon. Mix until smooth.

Preheat the oven to 350°F (175°C).

Scoop a tablespoon of cookie dough and flatten it in your hand. Place a teaspoon of the carrot cake filling in the center and fold the dough around it, sealing it completely.

Place the stuffed cookies on a baking sheet lined with parchment paper.

Bake for 12-15 minutes or until the edges are golden brown. Allow to cool on the baking sheet for a few minutes before transferring to a wire rack.