Preheat oven to 350°F (175°C).

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

Beat in the eggs one at a time, then mix in the grated carrots and oats.

In a separate bowl, combine the flour, baking soda, cinnamon, nutmeg, and salt.

Gradually add dry ingredients to the carrot mixture and mix until just combined.

Drop spoonfuls of dough onto a baking sheet lined with parchment paper.

Bake for 12 minutes, or until the edges are lightly golden. Let cool on the baking sheet for a few minutes before transferring to a wire rack.

To make the cream filling, beat the softened cream cheese, softened butter, powdered sugar, and vanilla extract until smooth and creamy.

Once cookies are cool, spread the cream filling on the flat side of one cookie and sandwich with another cookie.