Preheat oven to 350 degrees F (176 C) and line a standard muffin holder with 12 paper liners (as original recipe is written // adjust if altering batch size).
Add non-dairy milk and vinegar or lemon juice to a large mixing bowl and let set a few minutes to curdle/activate. Then add oil and vanilla and whisk or use a hand mixer to beat vigorously to combine. Then add sugar and whisk or use a hand mixer to beat to combine/dissolve. It may splash so be careful!
Add dry ingredients (omitting sprinkles) to a sifter in this order: two-thirds of the flour, baking powder, baking soda, salt, and then the remaining third of the flour.
Sift over wet ingredients and use a whisk or hand mixer to blend until well incorporated and no large lumps remain. The texture should be somewhere between thick and thin. Not liquidy, but not scoopable (rather, pourable). Somewhere near a buttermilk pancake batter consistency. We had to add another 1-2 Tbsp flour to thicken slightly.
Add sprinkles and gently fold/stir with a rubber spatula or mixing spoon. Then divide batter evenly among cupcake holders making sure NOT to overfill. These do best at 3/4 of the way up.
Bake on a center rack for 20-24 minutes, or until a toothpick inserted into the center comes out clean. They will only have a very, very slight golden brown color.
Let cool completely on a cooling rack. In the meantime, prepare frosting (optional). Wipe clean your mixing bowl and add softened butter. Beat until light and fluffy. Then add vanilla and mix once more.
Add SIFTED powdered sugar 1/2 cup at a time and continue mixing until thick and creamy. Scrape down sides as needed. If it gets too thick or crumbly, add a splash non-dairy milk to thin (optional). You want this frosting to be very thick so it will hold its shape once on the cupcakes. If it gets too thin, thicken with more powdered sugar.
Once cooled, frost cupcakes and top with sprinkles. Serve immediately. Store leftovers covered at room temperature or refrigerated up to 3 days.
*Some brands of sprinkles aren't vegan friendly, so be sure to check! *Nutrition information is a rough estimate calculated with frosting.