Make the Cupcakes: Preheat oven to 350 degrees F. Line a standard muffin pan with paper cupcake liners.
Sift the cake flour, sugar, baking powder, baking soda, and salt in a large mixing bowl.
In a medium bowl, whisk together ¼ cup of the milk, the sour cream, the egg, and the egg white; set aside.
Beat the dry ingredients on low speed for 15 seconds to combine.
Add the butter, vanilla, and remaining ¼ cup of the milk. Mix on medium speed until the dry ingredients are moistened, about 1 minute. Scrape down the sides and bottom of the bowl.
With the mixer on medium speed, add the wet ingredients in 3 additions, beating for 15 seconds after each addition. Scrape down the sides of the bowl and beat for an additional 15 seconds. It’s okay if there are some lumps, do not overmix!
Divide the batter evenly between muffin cups. Bake until a toothpick inserted in the center comes out clean, about 20 to 25 minutes. Cool for 15 minutes in the pan, then turn out to a wire rack to cool completely.
Make the Vanilla Frosting: Using the whisk attachment of your stand mixer, whip the butter on medium-high speed for 5 minutes, stopping to scrape the bowl once or twice.
Reduce the speed to low and gradually add the powdered sugar. Once all of the powdered sugar is incorporated, increase the speed to medium-high and add the vanilla, mixing until incorporated. Whip at medium-high speed until light and fluffy, about 2 minutes, scraping the bowl as needed. Frost cupcakes as desired. The cupcakes can be stored at room temperature in an airtight container for up to 4 days.
Mini Cupcakes: To make mini cupcakes, follow the directions above and divide the batter evenly into the wells of a 24-cup mini muffin pan. Bake for 9 to 14 minutes.
Doubling the Recipe: To make 24 cupcakes, use ⅓ cup sour cream, 3 whole eggs, and double the remaining ingredients.
9x13-inch Cake: Double the recipe per directions above and bake for 28 to 35 minutes.
9-inch Layer Cake: Double the recipe per directions above, divide the batter between two greased and floured 9-inch cake pans, bake for 18 to 22 minutes.
Cupcake Storing: Keep your frosted vanilla cupcakes in an airtight container for up to 4 days.
Frosting storage: You can store the frosting in the refrigerator in an airtight container for up to 3 days. Let it come to room temperature and then give it a quick whip in the mixer before using.
Freezing: Wrap unfrosted cupcakes in plastic wrap and keep in a freezer-safe ziplock bag for up to 3 months. Leave wrapped to thaw on the counter. Allow to come to room temperature before unwrapping and frosting.