How to Make It
To prepare cupcakes, preheat oven to 350°F. Line 18 muffin cups with liners; coat with baking spray. Place beet in a saucepan; cover with water. Bring to a boil over medium-high; boil until beet is tender when pierced, about 15 minutes. Drain; cool 10 minutes.
Process beet in a food processor until very finely chopped. Remove 1 cup beet from processor; reserve remaining beet for another use. Return 1 cup reserved beet to food processor; add buttermilk and vanilla. Process until very smooth.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Whisk together flour, cocoa, baking powder, and 1/2 teaspoon salt in a bowl.
Beat granulated sugar, oil, and 1/4 cup butter in a large bowl with an electric mixer on medium speed until fluffy, about 5 minutes. Add eggs and egg white, 1 at a time, beating well after each addition. Add flour mixture and beet mixture alternately to butter mixture, beginning and ending with flour mixture. Divide batter among prepared muffin cups. Bake 18 to 20 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack for 10 minutes. Remove cupcakes from pan; cool completely on wire rack, about 30 minutes.
To prepare frosting, beat yogurt, 2 tablespoons butter, dash of salt, and cream cheese in a medium bowl with a mixer on high speed until smooth. Add powdered sugar; beat on low speed 1 minute or just until combined. (Do not overbeat.) Spread frosting evenly onto cupcakes.