Preheat the oven to 175°C (350°F) and prepare a sheet cake pan with grease and parchment paper.
Mix flour, baking powder, and salt in a bowl.
Beat butter and sugar until light and fluffy, then add eggs, vanilla extract, lemon zest, and lemon juice.
Add dry ingredients gradually with milk, mixing until a smooth batter forms.
Pour the batter into the prepared sheet pan and bake for 25–35 minutes until a toothpick comes out clean.
Prepare lemon glaze or frosting by combining powdered sugar with lemon juice and spread over the cooled cake.
Garnish with lemon zest and slice into squares before serving.