Make three depressions in the batter. 2 smaller depressions and 1 large one (see photo).
Pour vinegar and vanilla in the two smaller depressions and the vegetable oil in the larger depression.
1 teaspoon white vinegar, 1 teaspoon vanilla extract, 1/4 cup vegetable oil
Pour the cup of water over the entire mixture and whisk together until batter forms.
1 cup water
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, make the buttercream.
In the bowl of a stand mixer or a hand mixer and glass bowl, cream together butter and powdered sugar until combined. Add milk then vanilla bean paste and beat until light and fluffy. Set aside.