Step 1: In a large bowl, cream together 1 cup softened unsalted butter, brown sugar, and granulated sugar until light and fluffy.
Step 2: Beat in the eggs one at a time, then stir in 1 tsp vanilla extract until well combined.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, baking soda, salt, ground cinnamon, ground ginger, ground nutmeg, and ground cloves.
Step 4: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Step 5: Fold in the rolled oats and finely grated carrots until evenly distributed.
Step 6: Cover the dough and chill in the refrigerator for at least 30 minutes, or up to 2 hours.
Step 7: Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper.
Step 8: Drop rounded tablespoons of chilled dough onto the prepared baking sheets, leaving about 2 inches between each cookie.
Step 9: Bake for 10-12 minutes, or until the edges are lightly golden and the centers are set. Let cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.
Step 10: While cookies cool, prepare the cream cheese frosting. In a large bowl, beat the softened cream cheese and 1/2 cup softened unsalted butter until smooth and creamy.
Step 11: Gradually add the sifted powdered sugar, 1 tsp vanilla extract, and a pinch of salt, beating until light and fluffy.
Step 12: Once cookies are completely cool, spread a generous amount of cream cheese frosting on the flat side of one cookie and top with another cookie to form a sandwich. Repeat with remaining cookies and frosting.