Preheat the oven to 375°F (190°C). Line a 15×10-inch jelly roll pan with parchment paper and lightly grease it.
In a large bowl, beat the eggs and granulated sugar together with an electric mixer on high speed until thick and pale, about 5 minutes.
Add the vegetable oil and vanilla extract to the egg mixture and mix until combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Gradually fold the dry ingredients into the wet ingredients until just combined.
Gently fold in the grated carrots, chopped walnuts, and raisins.
Pour the batter evenly into the prepared jelly roll pan and spread it out smoothly.
Bake for 12 to 15 minutes, or until the cake springs back when lightly touched and a toothpick inserted in the center comes out clean.
While the cake is baking, lay a clean kitchen towel on a flat surface and dust it generously with powdered sugar.
Once the cake is done, immediately loosen the edges with a knife and invert the cake onto the prepared towel. Carefully peel off the parchment paper.
Starting from the short end, roll the cake up with the towel inside. Let it cool completely on a wire rack while rolled.
To make the frosting, beat the cream cheese and butter together until smooth and creamy.
Add the powdered sugar and vanilla extract and beat until well combined and fluffy.
Once the cake is completely cool, gently unroll it and spread the cream cheese frosting evenly over the surface.
Roll the cake back up without the towel, wrap it tightly in plastic wrap, and refrigerate for at least 1 hour before serving.
Slice and serve chilled.