Preheat your oven to 375°F. Line a 15 x 10-inch jelly roll pan with parchment paper, allowing about 1 inch to extend beyond the sides. This extra parchment will make it much easier to lift the cake out once baked.
In a large mixing bowl, whisk together the flour, cinnamon, baking powder, ginger, salt, and nutmeg until evenly distributed.
In another large bowl, whisk the eggs with both sugars for about 1 minute, until nicely blended. Add the oil, vanilla, finely ground walnuts, and shredded carrots. Whisk gently until everything is evenly combined.
Using a rubber spatula, gradually fold the dry ingredients into the carrot mixture. Stir gently, just until the flour disappears and the batter comes together. Avoid overmixing to keep the cake soft and tender.
Pour the batter into the prepared pan and spread it into an even layer, making sure it reaches the corners. Bake for 10 to 13 minutes, or until the surface springs back when gently touched.
Remove the cake from the oven and carefully transfer it to a flat work surface. While it is still hot, gently roll it up from one short end to the other. Place the rolled cake seam-side down on a wire rack and allow it to cool completely to room temperature.