Preheat the oven to 355F (180C). Line an 8x8 square baking pan with parchment paper.
Combine the milk and white vinegar. Let it sit for 5 minutes to thicken slightly.
In a large bowl, use a hand mixer or stand mixer fitted with a paddle attachment to cream the softened butter and sugar together. Beat on medium speed until the mixture is light and fluffy.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
Add the flour, baking powder, salt, and cornstarch. Beat on medium speed for 1 minute until the dry ingredients are fully incorporated.
Add the milk and vinegar mixture. Beat until combined (don't over beat).