Preheat your oven to 350°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, mix the granulated sugar, brown sugar, and vegetable oil until well combined. Add the eggs one at a time, mixing well after each addition. Stir in the grated carrots, crushed pineapple, and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a tablespoon or a cookie scoop, drop rounded tablespoons of batter onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 12-15 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean. Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
While the cookies are cooling, prepare the cream cheese filling. In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy. Gradually add the powdered sugar and vanilla extract, mixing until well combined.
Once the cookies are completely cool, spread a generous amount of cream cheese filling on the flat side of one cookie and top with another cookie to create a sandwich. Repeat with the remaining cookies.
Serve immediately or refrigerate for up to 3 days.