Prepare the Sponge Cake: Preheat oven to 350°F (175°C). Grease a 9-inch round cake pan. Cream butter and sugar until fluffy, about 4-5 minutes. Add eggs one at a time, then vanilla.
Mix Dry Ingredients: In separate bowl, whisk flour, baking powder, and salt. Alternate adding dry ingredients and milk to butter mixture, beginning and ending with flour.
Add Lemon Flavor: Gently fold in lemon juice and zest. Pour batter into prepared pan and bake 25-30 minutes until golden and toothpick comes out clean.
Cool the Cake: Let cake cool completely in pan, then turn out onto wire rack. Once cool, slice horizontally into two even layers.
Make Custard Base: In heavy saucepan, heat milk and cream over medium heat until just simmering. In separate bowl, whisk egg yolks, sugar, and cornstarch until pale and thick.
Temper the Eggs: Slowly pour ⅓ of hot milk mixture into egg yolk mixture while whisking constantly to prevent scrambling.
Cook the Custard: Return mixture to saucepan and cook over medium-low heat, stirring constantly, until it coats the back of a spoon (about 5-7 minutes).
Finish the Custard: Remove from heat and immediately stir in lemon juice, butter, and vanilla. Strain through fine-mesh sieve if needed. Cool completely.
Assemble the Cake: Place bottom cake layer in clean 9-inch pan. Pour cooled custard over cake, spreading evenly. Top with second cake layer.
Final Baking: Bake assembled cake at 325°F (163°C) for 25-30 minutes until custard is just set and doesn't jiggle when gently shaken.
Cool and Chill: Let cake cool completely, then refrigerate for at least 2 hours or overnight for best texture and flavor development.
Serve: Dust with powdered sugar and garnish with fresh lemon slices and mint. Cut with sharp knife dipped in warm water between slices.