Preheat oven to 180 degrees Line a 12-cup muffin tin with muffin cases. Line a second muffin tin with 4 cases or alternatively line a mini muffin tin with 10 cases.
In a bowl combine cornstarch, flour, baking powder, baking soda and salt and set aside.
In a large bowl beat together butter, oil and sugar until homogeneous. Add eggs, one at a time. Add in vanilla, cider and yogurt and mix until smooth. Gradually add the dry ingredients and mix at a lower speed, just until incorporated in the batter.
Spoon the batter into the muffin cases filling them 2/3 full. Bake for about 20-25 minutes or until a toothpick inserted in the center comes out clean. Remove the pan from the oven, let the cupcakes cool for 2-3 minutes and then transfer them to a wire rack. Frost them after they cool down to room temperature.