First, set your oven to 350°F (175°C). Take a 10×15-inch jelly roll pan, grease it well, then line it with parchment paper and give the parchment a light greasing too. Spread out a clean kitchen towel on your counter and sprinkle it generously with powdered sugar—this will keep the cake from sticking when you roll it later.

In a medium bowl, whisk the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. In a larger bowl, beat the eggs with the granulated sugar until the mixture looks pale and slightly thick, about 2–3 minutes. Stir in the oil and vanilla. Add the dry mixture and mix just until it comes together, then gently fold in the shredded carrots.

Pour the batter into the prepared pan, spreading it evenly. Bake for 13–15 minutes, or until the cake springs back when lightly pressed and a toothpick comes out clean.

As soon as it comes out of the oven, run a knife around the edges to loosen it. Carefully flip the cake onto the prepared towel and peel away the parchment paper. Starting from the short side, roll the cake up with the towel. Let it cool completely while rolled, about 30 minutes.

While the cake cools, beat the softened cream cheese and butter until smooth and creamy. Add the powdered sugar and vanilla, beating until fluffy and well blended.

When the cake is fully cooled, gently unroll it. Spread the cream cheese filling evenly across the surface, all the way to the edges. Roll it back up, this time without the towel, and wrap it tightly in plastic wrap.

Chill in the refrigerator for at least 30 minutes before serving. Sprinkle powdered sugar on top if you like, then slice into rounds and enjoy.