Preheat oven to 180 °C (350°F) conventional and grease two 8-inch cake tins. Also, line the bottoms with parchment paper.

Sift together flour, cornstarch, baking powder and salt. Using a whisk, mix until well combined and set aside.

In a large bowl add in butter, vegetable oil, sugar and lemon zest. Using a hand or stand mixer on medium speed, cream together for two minutes until light and creamy.

Add in eggs one by one, mixing well in between each addition.

Add the milk, yogurt, and lemon juice. Mix until well combined—the batter may look curdled, but that's okay.

Add your pre-sifted dry ingredients to the wet mixture. Using a spatula, gently fold until just combined—do not overmix. Finally, add the poppy seeds and mix until just combined.

Distribute the batter evenly into the two 8-inch cake tins, and bake for 33 minutes or until a toothpick comes out clean or with a few moist crumbs on it.

Once baked, allow the cake layers to cool in the cake tins for about 15-20 minutes, and then turn them out onto a wire rack to completely cool.

In a large bowl, add the unsalted butter. Using an electric mixer, cream it on medium-high speed for a few minutes until light and fluffy.

Add in the powdered sugar in 3 batches while mixing on low. Ensure that each batch of powdered sugar is mixed into the butter well before adding in the next batch.

Next add in your cold cream cheese, vanilla and fresh lemon juice and mix on a medium speed just until the frosting is smooth. Avoid over-mixing.