Whisk the butter and sugar together until frothy, then add the eggs and lemon zest one after the other. Then stir in the baking powder and flour, pour the dough into a springform pan (20 cm) and bake for about 35 minutes.
In the meantime, heat the lemon juice and the lemon zest with the sugar in a saucepan and bring to the boil for 1 minute.
Take the cake out of the oven and immediately - while still warm - brush with the lemon syrup. Let cool completely in the tin.