Preheat oven to 350°F. Line a cupcake pan with 12 standard size baking cups (24 minis).
In a measuring cup, stir together half & half, vinegar, vanilla extract, and egg yolk. Set aside and let come to room temp (about 30 minutes).
In a large stand mixer bowl, sift together the cake flour, sugar, baking powder, baking soda, and salt. Add butter and vegetable oil and mix on low until moistened. Add 1 tbsp of wet mixture and increase speed to medium, mix for about 45 seconds.
On low speed, slowly pour in the half of the remaining wet mixture then beat on medium for 20 seconds. Repeat for remaining half. Scrape down sides.
In dry glass bowl, beat the egg whites until you achieve foamy white peaks. Using a spatula, gently fold the whipped egg white into your batter, in two additions.
Distribute all of the batter between the baking cups filling about 3/4 the way full. Bake standard cups for 15-17 minutes (minis for 8-10) or until your finger leaves a slight impression or a toothpick comes out with a few moist crumbs. Let cool before frosting.