Preheat the oven to 350 degrees, and fill the cupcake pan with liners.
In a medium-sized bowl, combine the flour, cornstarch, baking soda, baking powder, and salt. Mix well. Set this bowl off to the side.
In a mixer bowl, cream the butter and sugar until it is light and fluffy.
Now add the oil to the butter and sugar mixture, mixing well.
Add in the eggs, one at a time mixing well until each is completely incorporated before you add the next.
Add in the vanilla.
Next, in either a glass or a third small bowl, combine both kinds of milk, stirring to combine.
Slowly add the milk mixture and the flour mixture into the bowl that has the creamed butter, eggs and sugar mixture, alternating as you go and making sure it becomes completely incorporated. I like to let my mixer run for about 30 seconds, then scrape the edges of the bowl, and then let it run for 30 more seconds. This ensures that all ingredients are completely combined. You should now have a nice, smooth cupcake batter.
Using either a cookie scoop or a ¼ measuring cup and spoon fill the liners with the batter.
Bake at 350° for 21 minutes.