Preheat the oven to 170 degrees Celsius. Prepare the baking pan by lining it with baking paper.
Combine the dry ingredients in a bowl using a hand whisk: flour, cornstarch, baking powder, and salt.
Add both the sugars and lemon zest in a bowl and rub with your fingers to release the lemon oils into the sugar.
Add the softened butter and whisk on high speed for 3-5 minutes using an electric or stand mixer until the mixture becomes pale and creamy.
Add the egg and egg yolk into the batter, one at a time, and whisk on low speed for 30 seconds after every addition. Then, add the vanilla essence and whisk for another 30 seconds until well combined.
Add the yogurt to the batter and whisk for 1-2 minutes on medium speed until it's fully combined. The batter may appear split at this point, but it will come together once you add the dry ingredients.
Add the dry ingredients and fold in the batter slowly using a silicone spatula, and mix until just combined. Don't rush this process, you want the batter to retain as much air as possible.
Layer the lemons: Mix the brown sugar and lemon juice and pour it into the bottom of the prepared cake pan. Peel and cut the lemons into medium-sized slices, de-seed as best as possible, and place on top of the brown sugar mix, starting from the center of the pan.
Place the cake batter on top of the lemon layer and bake for 30-40 minutes until the cake is fully cooked through the center. Let it cool for 30 minutes before removing from the pan and enjoy.