Make the Cheesecake Filling
Preheat the oven to 325°F (165°C). Butter and line a jelly roll pan with parchment. This can be 10x15-inches (25x38cm) or 11x17-inches (28x43cm). Either will work.
In a stand mixer with a paddle attachment, beat the cream cheese, sugar and sour cream on medium-high speed until very smooth and lump-free, roughly 3-4 minutes.
Add the egg and vanilla and whip to combine. Stir a few times with a rubber spatula to ensure even mixing.
Spread the cheesecake evenly into your prepared pan. Set aside.
Make the Carrot Cake
Back on the standmixer, add the whisk attachment. Whip the eggs, sugar, oil and vanilla on high speed until thick and pale, roughly 4-5 minutes.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger and nutmeg, and mix into the wet ingredients until evenly mixed.
Finally fold in the carrots until just combined. Carefully spread the batter over the cheesecake filling using a palette knife. Take care not to mix the two layers together.
Bake for around 25 minutes, until the cake springs back when pressed. Set aside to cool in the pan for just 10 minutes. You need it warm to roll it.
Rolling The Cheesecake Roll
Once the cake has cooled but is not cold, dust it with powdered sugar.
Place a piece of parchment paper on top of the cake and place another baking sheet on top of the parchment so that the bottom of the pan is on the cake.
Very carefully lift up both pans and flip them over (use oven mitts if the pan is too hot).
Gently lift the top pan to release the cake. The cheesecake side should now be face up. Carefully remove the parchment paper from the cheesecake.
While the cake is still warm, and using the bottom piece of parchment paper to help guide the cake, slowly and carefully roll up the cake from the shorter side (see video). Take your time at the beginning to roll the cake tightly to prevent any gaps in the center.
Once your cake is rolled, let it sit on it’s seam in the parchment for 2 minutes to help it retain its shape while it cools to room temperature.
To serve, remove the parchment, trim both ends and place on a serving plate. Dust with more powdered sugar. Store leftovers covered in the fridge for up to 3 days.