1. Lemon Curd: In a saucepan, whisk together sugar, egg yolks, and cornstarch until smooth. Add lemon zest and juice. Cook over medium heat, stirring constantly near the end, until thickened (about 8-10 minutes on gas stovetop, up to 20 minutes on electric). Remove from heat, stir in butter until melted. Transfer to a container, cover, and chill thoroughly before use.
2. Cake: Preheat oven to 350°F (175°C). Grease and line a 9×13-inch pan with parchment paper. Whisk together flours, baking powder, baking soda, salt, and poppy seeds. In a large bowl, rub lemon zest into sugar to release oils. Add oil, melted butter, eggs, lemon juice, and vanilla, whisking until combined. Add half the dry ingredients and mix until incorporated. Stir in milk and sour cream, then add remaining dry ingredients, mixing gently until smooth. Avoid overmixing to prevent a dense cake.
3. Pour batter into pan and bake for 30-35 minutes, until a toothpick inserted in the center comes out with a few moist crumbs. Let cool completely on a wire rack.
4. Frosting: Beat cream cheese and butter until creamy and smooth. Gradually add powdered sugar, mixing well after each addition. Stir in vanilla extract. Spread frosting evenly over cooled cake.
5. Spoon about three-quarters of the chilled lemon curd in small dollops on top of the frosting and swirl gently with a knife or spatula. Sprinkle with additional poppy seeds for garnish.