Preheat your oven to 350°F (175°C). Line a 10x15 inch jelly roll pan with parchment paper and lightly grease the paper.
In a medium bowl, whisk together the flour, baking powder, cinnamon, and nutmeg.
In a large bowl, beat the eggs and granulated sugar on high speed until thick and pale, about 3-5 minutes. Add the vanilla extract and beat to combine.
Fold in the grated carrots, then gently fold in the dry ingredients until fully combined.
Pour the batter into the prepared pan, spreading it evenly. Bake for 12-15 minutes or until a toothpick inserted into the center comes out clean.
While the cake bakes, prepare a kitchen towel dusted generously with powdered sugar.
Once baked, immediately turn the cake onto the towel. Peel off the parchment paper and roll the cake up in the towel, starting from a short end. Let it cool completely.
For the filling, beat the cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
Once the cake is cool, unroll it gently, spread the cream cheese mixture evenly over the surface, and roll it back up.
Wrap the roll in plastic wrap and refrigerate for at least 1 hour before slicing and serving. Dust with additional powdered sugar if desired.