Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a large bowl, beat together the granulated sugar, brown sugar, and vegetable oil until well blended.
Add the eggs, one at a time, mixing well after each addition, then mix in the vanilla extract.
Fold in the grated carrots with a spatula until evenly distributed.
Scoop tablespoon-sized amounts of batter onto the prepared baking sheets, leaving space between each.
Bake in the preheated oven for 12-15 minutes, or until the edges are set and the tops spring back when lightly touched.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
In a bowl, beat together the cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
Assemble the whoopie pies by spreading a generous amount of the cream cheese filling onto the flat side of one pie, then topping it with another pie to form a sandwich.
Serve immediately, or chill in the refrigerator for a bit for a firmer filling.