Preheat the oven to 180 °C and line a muffin pan with cupcake holders.
To make the batter, cream the butter and castor sugar until light and fluffy. Add the eggs, one at a time, beating well after each addition. Sift the flour with the baking powder and salt and then add this to the butter-egg mixture. Continue to beat and slowly add the oil, then the milk. Beat well. Add the vanilla essence, lemon essence and lemon zest, and beat for a further minute.
Divide the batter between the cupcake holders and bake for 18 to 20 minutes. Transfer to a wire rack and allow to cool completely. To make the icing, beat the butter until light and fluffy. Add the vanilla essence, lemon juice and lemon zest, and beat for a further minute. Add the icing sugar and beat to combine. Ice the cooled cupcakes and serve.
Extract from Gourmet Sisters: sharing food and friendship, by Sue-Anne Allen and Ilse Fourie.