Whisk together the flour, baking powder and salt in a bowl and set aside.
Using an electric mixer on medium speed, beat the butter and sugar until light and fluffy, about 5 minutes. Add egg and vanilla and beat again until combined.
Alternately add the milk and dry ingredients, mixing well between each addition. Once you are done adding the dry ingredients and the milk, fold in the lemon zest.
Pour batter into a prepared 8 x 8 baking dish. Bake for 30-40 minutes or until a toothpick inserted in the center of the cake comes out clean.
Frosting
Combine butter and cream cheese in a mixing bowl and use an electric mixer to combine until smooth. Add powdered sugar, salt, lemon juice and lemon zest and continue using the electric mixer to beat until smooth.
Once the cake has cooled, generously frost. Decorate with candied lemon peel, sprinkles or more lemon zest.