Preheat the oven to 350°F. Line a 15×10-inch jelly roll pan with parchment paper, leaving some overhang.

In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt.

In a large bowl, beat the eggs and sugars until thick and creamy, about 3-4 minutes. Add the vanilla extract and mix until combined.

Gradually add the flour mixture to the egg mixture, beating until just combined. Fold in the grated carrots and walnuts, if using.

Pour the batter into the prepared pan and spread it evenly. Bake for 10-12 minutes, or until the cake springs back when lightly touched.

While the cake is baking, dust a clean kitchen towel with powdered sugar. Once the cake is done, immediately turn it out onto the prepared towel. Carefully peel off the parchment paper.

Starting from a short end, roll the cake up in the towel. Let it cool completely on a wire rack.

In a medium bowl, beat the cream cheese, powdered sugar, butter, and vanilla extract until smooth and creamy.

Once the cake is cool, carefully unroll it and spread the cream cheese filling evenly over the cake.

Roll the cake back up without the towel and wrap it in plastic wrap. Refrigerate for at least 1 hour before slicing and serving.