In a large bowl, beat the sugar and butter until creamy and pale. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed. Add vanilla and mix to combine.
Combine milk and vinegar in a small bowl. Set aside.
Add the flour alternately with milk to the butter mixture, beginning and ending with the flour. Scrape down the mixing bowl with a spatula and turn the batter over several times to ensure all of the ingredients are well incorporated. Beat just until incorporated. Do not overmix this batter.
Pour the cake mixture into the prepared pans (2 1/2 cups of batter in each pan approximately).
Bake for 20 - 25 minutes, or until a skewer comes out clean when poked in the center.
To bake in a 9x13 pan: Simply pour the batter into a greased and lightly floured 9x13 pan and bake for 30 – 35 minutes or until a toothpick inserted in the center comes out clean.
Cakes can be baked ahead, cooled, and covered tightly at room temperature overnight or up to 2 days in the refrigerator.
To make your own self-rising flour combine for each cup of all-purpose flour, add 1 1/2 teaspoons of baking powder and 1/4 teaspoon of salt. For this recipe, you'll need to combine 4 cups of all-purpose flour + 6 teaspoons of baking powder + 1 teaspoon salt.
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Please note that nutritional information is a rough estimate and it can vary depending on the products used.