Preheat the oven to 350 degrees F. Oil the bottom and sides of two 9-by-2-inch round cake pans. Flour the pans and tap out the excess.
Whisk the flour, cornstarch, baking powder, baking soda and salt in a medium bowl. Combine the milk, vinegar and vanilla in a small bowl.
Beat the butter, oil and sugar in a large bowl with a mixer on medium-high speed until fluffy, 5 to 7 minutes. Beat in the eggs one at a time; beat until thick, 3 minutes. Reduce the speed to medium low; beat in the flour mixture in three batches, alternating with the milk mixture. Beat just until smooth, then finish mixing with a rubber spatula. Divide the batter between the pans.
Bake the cakes until lightly browned and the centers spring back when lightly pressed, 35 to 45 minutes. Transfer to a rack and let cool 15 minutes in the pans. Loosen the edges with a knife and turn out the cakes onto the rack; let cool completely.