Combine the brown sugar, granulated sugar and eggs in a bowl and whisk for 1–2 minutes until slightly foamy. Add the oil and mix until smooth.
Meanwhile, coarsely grate the apples with the skin on and drizzle the lemon juice over them.
Add the grated apples to the egg mixture and mix well.
In another bowl, mix the flour, cornstarch, baking powder, baking soda, cinnamon, ginger, cardamom and salt. Add the dry ingredients to the batter and fold them in with a spatula.
Divide the batter into 3 equal portions and transfer to 18 cm cake pans lined with baking paper.
Bake at 160°C for 25–30 minutes.
Let the sponges cool and level them if needed.
Wrap them in plastic wrap and keep them in the fridge until assembling.