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

Sift together flour, cornstarch, baking powder, and salt. Mix until well combined and set aside.

In a large bowl, add butter, vegetable oil, sugar, and lemon zest. Cream together for two minutes until light and creamy using a mixer.

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

Add milk, yogurt, and lemon juice. Mix until well combined, even if the batter looks curdled.

Gently fold the pre-sifted dry ingredients into the wet mixture until just combined. Avoid overmixing.

Add the poppy seeds and mix until just combined. Distribute the batter evenly into the cake tins.

Bake for 33 minutes or until a toothpick comes out clean or with a few moist crumbs.

Allow the cake layers to cool in the tins for 15-20 minutes, then turn them out onto a wire rack to cool completely.

For the frosting, cream unsalted butter in a bowl until light and fluffy.

Gradually add powdered sugar in 3 batches while mixing on low until well combined.

Add cream cheese, vanilla, and fresh lemon juice. Mix until the frosting is smooth, avoiding overmixing.