Preheat the oven to 350°F (175°C) and grease a cake pan.
In a large mixing bowl, cream together the softened butter and sugar.
Add in the eggs one at a time, mixing well after each addition.
Combine the flour and baking powder in a separate bowl, then gradually add to the wet mixture along with the milk.
Pour the batter into the prepared cake pan and bake for 25-30 minutes, or until a toothpick comes out clean.
While the cake cools, prepare the custard by combining milk, cornstarch, sugar, and vanilla in a saucepan over medium heat.
Continue to stir the custard until it thickens, then remove it from heat and let it cool.
Once the cake is completely cool, split it in half horizontally. Spread a layer of custard on the bottom half, then add sliced strawberries on top.
Place the second layer of cake on top and frost it with the remaining custard. Dust with powdered sugar before serving.