Preheat oven to 180° C. Line the cupcake pans with liners.
In a large bowl, beat the sugar and butter until creamy and pale. Add vanilla and mix to combine.
Combine milk and vinegar in a small bowl.
Add the flour alternately with milk, beginning and ending with the flour mixture; beat until smooth.
Divide batter evenly among liners, about three-quarters full each.
Bake for 18-22 minutes, or until a toothpick inserted in the center comes out clean. IMPORTANT: these cupcakes won't brown as the cupcakes made with eggs, so when you see the top set check the cupcakes for doneness with the toothpick test. Let them cool in the pan for a couple minutes, then remove. Allow cooling completely before frosting.
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