Preheat your oven to 350°F (175°C).
In a bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, mix the granulated sugar, brown sugar, and oil until combined.
Add the eggs and vanilla extract to the sugar mixture, beat until well-incorporated.
Gradually add the dry mixture to the wet ingredients, mixing until just combined.
Fold in the grated carrots gently.
Scoop tablespoons of batter onto a lined baking sheet, spacing them about two inches apart.
Bake for 12-15 minutes or until the edges are golden.
Let the cookies cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.
While the cookies cool, prepare the cream cheese filling.
In a bowl, beat the softened cream cheese, powdered sugar, and vanilla extract until smooth.
Scoop a generous tablespoon of cream cheese filling onto the flat side of a cookie, and top with another cookie to create a sandwich.
Repeat until all cookies are filled.
Serve immediately or refrigerate for a couple of hours for the flavors to meld.