Line the base of a deep 20cm/9in square cake tin with non-stick paper and preheat the oven to180C/160C Fan/Gas 4.
Melt the butter over a low heat in a small pan, pour it into a bowl with the sugar, oil, cornflour (or arrowroot or cocoa) and vanilla. Beat well until smooth, then whisk in the eggs followed by the milk and cream.
Sift and beat the flour and baking powder into the butter mixture in batches until smooth, then spoon into the prepared tin and bake for 50-60 minutes (for a large cake). Keep a careful eye toward the end of the cooking time, and cover with foil if the cake is getting too dark. For cupcakes, fill the papers about three-quarters full then bake for about 20-25 minutes.
To vary the flavour, replace the milk with orange juice for a citrus cake; or add finely grated zest, chocolate chips or dried fruit in with the milk.