In a bowl, mix cream cheese, sugar, and vanilla until smooth. Chill the filling while preparing the cookies.
In another bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, and nutmeg.
In a separate large bowl, cream the butter, brown sugar, and granulated sugar until fluffy.
Mix in the grated carrots, vanilla, and egg until combined.
Gradually fold in the dry ingredients until a soft dough forms. Chill for 30 minutes.
Preheat oven to 350°F and line a baking sheet with parchment paper.
Drop spoonfuls of dough onto the sheet and bake for 10-12 minutes, until edges are golden.
Cool completely before assembling the sandwiches.
Spread or pipe the cheesecake filling onto one cookie and top with another to create a sandwich.
Refrigerate for 15 minutes before serving for the best texture.