Preheat oven to 375°F (190°C). Grease a 10x15-inch jelly roll pan and line with parchment paper, then grease the parchment.

In a large bowl, beat eggs and sugar with an electric mixer on high speed for 5 minutes until thick and lemon-colored.

Stir in the vegetable oil, 1 teaspoon vanilla, and the finely grated carrots.

In a separate bowl, whisk together flour, baking powder, cinnamon, ginger, nutmeg, and salt.

Gently fold the dry ingredients into the egg mixture until just combined.

Spread the batter evenly into the prepared pan. Bake for 12 to 15 minutes or until the top of the cake springs back when touched.

Immediately invert the cake onto a clean kitchen towel dusted with powdered sugar. Remove parchment paper.

Starting at the short end, roll up the cake and towel together. Let cool completely on a wire rack.

To make the filling, beat cream cheese and butter until smooth. Add 1 cup powdered sugar and 1/2 teaspoon vanilla; beat until light and fluffy.

Unroll the cooled cake and remove the towel. Spread the cream cheese filling evenly over the cake, leaving a 1/2-inch border.

Re-roll the cake. Wrap in plastic wrap and refrigerate for at least 1 hour before slicing.