1. Make the lemon curd: In a medium saucepan, whisk together sugar, egg yolks, and cornstarch until smooth. Add lemon zest and fresh lemon juice. Cook over medium heat, stirring constantly, until the mixture thickens and comes to a gentle boil. Remove from heat, stir in butter until melted and smooth. Transfer to a bowl and chill until set.

2. Preheat the oven to 350°F (175°C). Prepare a 9×13-inch baking pan by greasing and lightly flouring or lining with parchment paper.

3. Mix dry ingredients: In a large bowl, sift or whisk together all-purpose flour, cake flour (or flour and cornstarch), baking powder, baking soda, salt, and poppy seeds.

4. Combine wet ingredients: In a separate bowl, rub the lemon zest into sugar to release oils. Add vegetable oil, melted butter, eggs, lemon juice, and vanilla extract to the sugar mixture. Whisk until well combined.

5. Combine wet and dry: Add half of the dry ingredients to the wet mixture and whisk gently. Then add the milk and sour cream or yogurt mixture, mixing gently to combine. Add the remaining dry ingredients and fold until just smooth. Avoid overmixing to prevent a dense cake.

6. Bake: Pour batter into the prepared pan and smooth the surface. Bake for 30–35 minutes or until a toothpick inserted in the center comes out clean or with moist crumbs. Let the cake cool in the pan for 15–20 minutes, then transfer to a wire rack to cool completely.

7. Prepare the frosting: Beat cream cheese and butter on medium speed until smooth and creamy. Gradually add powdered sugar in batches, mixing well to avoid lumps. Add vanilla extract and lemon juice (if using), and beat until smooth and spreadable. If frosting is too soft, add more powdered sugar starting with ½ cup increments.

8. Assemble the cake: Spread a generous layer of cream cheese frosting on the cooled cake. Dollop chilled lemon curd over the frosting and gently swirl with a knife or skewer to create a marbled effect. Sprinkle additional poppy seeds on top as decoration.