In a large bowl, on the medium speed of an electric mixer, cream the butter until smooth. Add the sugar gradually and beat until fluffy, about 3 minutes. Add the eggs, 1 at a time, beating well after each addition. Add the dry ingredients in 3 parts, alternating with the milk, cream, vanilla and peppermint (you can mix the liquid ingredients together if you wish). With each addition, beat until the ingredients are incorporated but do not over beat. Using a rubber spatula, scrape down the batter in the bowl to make sure the ingredients are well blended. Carefully spoon the batter into the cupcake liners, filling them about 3/4 full. Bake for 20 to 25 minutes, or until a cake tester inserted into the center of the cupcake comes out clean.
Cool the cupcakes in tins for 15 minutes. Remove from the tins and cool completely on a wire rack before icing. This recipe will make about 2 dozen standard size cupcakes or about 48 mini cupcakes.