Preheat the oven to 350 degrees F and grease 2 - 8x8 round nonstick baking pans with butter.
Combine the milk with vinegar and allow to sit for 5 minutes to allow the milk to curdle.
Whisk together the flour, sugar, baking powder, and salt in a large mixing bowl. This is to remove any clumps.
Pour the oil, vanilla, and eggs into the milk mixture and then add to the dry ingredients in the large bowl. Mix until combined and then fold in the sprinkles.
Divide the cake between the two prepared cake pans and bake for 30-35 minutes or until a toothpick comes out with minimal crumbs.
Carefully remove from the oven and allow to cool for 15 minutes before removing from the pans. Allow to cool until ready to frost on a wire rack.
Buttercream
Beat the butter until nice and fluffy, and add in the powdered sugar, vanilla, and milk. Add more milk if the buttercream is too thick or more powdered sugar if the buttercream is too thin. If you're not using salted butter (most vegan butter is salted), you can add 1/4 teaspoon of salt.
To frost place one layer of the cake onto a cake plate level the cake and then cover the top with frosting. Level the other layer and then place on top of the frosted cake. Frost the entire cake and decorate as desired.
Notes
To make this a dairy free birthday cake we used Country Crock plant butter sticks for the buttercream and Silk next whole milk for the "milk".