Preheat oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners. In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt.

In a separate bowl, whisk non-dairy milk, oil, vanilla, and vinegar until smooth, about 30 seconds. Let it sit a minute.

Pour wet ingredients into the dry and stir just until no large flour pockets remain. Divide batter among liners, filling ⅔ full, and bake 18 to 22 minutes until a toothpick comes out clean. Cool in pan 5 minutes, then transfer to a rack to cool completely.

For the frosting, beat vegan butter until creamy, about 2 minutes. Slowly add powdered sugar, then vanilla and 2 tbsp milk. Beat on medium-high for 3 to 4 minutes until fluffy, adding more milk if too stiff.

Once cupcakes are completely cool, frost with a piping bag or knife and serve.