1. Prepare the Cake:

1. Preheat oven to 350°F (175°C). Grease a 9×13-inch baking dish.
2. In a bowl, whisk together eggs, sugar, and lemon zest until light and fluffy.
3. Add milk, oil, lemon juice, and vanilla extract, mixing well.
4. Sift in flour, baking powder, and salt, folding gently to combine.
5. Pour the batter into the prepared dish and bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
6. Let the cake cool completely.

2. Make the Lemon Cream:

1. In a saucepan, heat milk over medium heat until warm (do not boil).
2. In a separate bowl, whisk sugar, cornstarch, and egg yolks until smooth.
3. Slowly pour the warm milk into the egg mixture, whisking constantly.
4. Return mixture to the saucepan and cook over medium-low heat, stirring until thickened.
5. Remove from heat and stir in butter, lemon juice, zest, and vanilla. Let cool.

3. Assemble the Cake:

1. Spread the lemon cream evenly over the cooled cake.
2. Refrigerate for at least 2 hours to allow the cream to set.

4. Serve & Garnish:

1. Slice into squares and top with whipped cream and lemon slices.
2. Dust with powdered sugar and serve chilled.