Preheat an oven to 350 degrees F.
and line the base of an 8-inch deep square baking tin with parchment paper.
In a large mixing bowl, whip
the butter and sugar with an electric beater until the mixture is pale and creamy, about 5 minutes. Beat in the lemon zest and vanilla. Add the eggs
, 1 at a time, beating until just combined after each addition. Fold in the flour in 2 batches until well combined. Spoon the batter
into the tin and bake for 40 to 50 minutes, or until a skewer
poked into the middle of the cake comes out clean. Cover the tin loosely with foil if the crust
browns too quickly.
Cool for 10 minutes before removing the cake from the tin and turning it out onto a wire rack to cool completely. Ice the pound cake
with the lemon butter icing.