In a stand mixing bowl, rub together the sugar and lemon zest. Then add the cake flour, baking powder, and salt and mix to combine.
Mix in the cubed butter until it resembles coarse sand.
Add the sour cream and oil and mix on low speed for exactly 1 minute. Scrape down the bowl.
In a bowl with a spout, whisk together the egg, milk, lemon juice, and vanilla. Slowly stream the liquid into the bowl with the mixer running on low until just combined. Scrape down the sides and bottom of the bowl to ensure everything is well combined.
Pour the batter into all three cake pans on top of the shortbread crust, about 225 g in each.
Dollop 1 ½ tablespoon of the lemon curd on top of the batter, use a toothpick to swirl it well into the batter.
Then bake the cake layers for 23-25 minutes, or until a toothpick inserted into the centers comes out covered in a few moist crumbs.
Lem them cool on a wire rack for 15 minutes, then flip them out of the pans. Allow them to cool completely before assembling.