Step 1: Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper.
Step 2: In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, ginger, and salt. Set aside.
Step 3: In a large bowl, using an electric mixer, cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.
Step 4: Beat in the egg until well combined, then stir in the vanilla extract.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Step 6: Gently fold in the finely grated carrots until evenly distributed throughout the batter.
Step 7: Drop rounded tablespoons of batter onto the prepared baking sheets, leaving about 2 inches between each. A small cookie scoop works best for uniform size.
Step 8: Bake for 10-12 minutes, or until the edges are set and the tops spring back when gently touched. Do not overbake.
Step 9: Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Step 10: While cookies cool, prepare the filling: In a medium bowl, beat the softened butter and cream cheese together until smooth and creamy, about 2-3 minutes.
Step 11: Gradually add the sifted powdered sugar, one cup at a time, beating on low speed until incorporated, then increasing to medium speed until light and fluffy. Beat in the vanilla extract until smooth. If the filling is too soft, chill for 15 minutes.
Step 12: Once cookies are completely cool, match them into pairs of similar size. Spread or pipe a generous amount of cream cheese filling onto the flat side of one cookie, then top with its matching partner. For easy storage, place them in an airtight glass food storage container.
Step 13: Repeat with the remaining cookies and filling. Serve immediately or store in the refrigerator.