Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

In a bowl, whisk together the flour, baking powder, and salt.

In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.

Beat in the eggs, one at a time, followed by the lemon zest, lemon juice, and vanilla extract.

Gradually add the dry ingredients to the butter mixture, alternating with milk, until just combined.

Divide the batter evenly between the prepared pans and smooth the tops.

Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.

Let cool in pans for 10 minutes, then remove from pans and cool completely on a wire rack.

In a saucepan, combine the milk, sugar, cornstarch, and egg yolks. Cook over medium heat, stirring constantly until thickened.

Remove from heat and stir in butter, vanilla, and lemon juice. Let cool.

Once the cakes are cooled, spread the custard filling on top of one layer, top with the second layer, and refrigerate for at least 30 minutes.

For the glaze, mix powdered sugar with lemon juice until smooth. Pour over the top of the cake.

Slice and serve!