How to Make It
Preheat oven to 350°F. Line 3 (12-cup) mini muffin trays with paper liners. Stir together all-purpose flour, white whole-wheat flour, cinnamon, baking soda, and salt in a bowl. Whisk together egg, egg yolk, grated carrots, brown sugar, crushed pineapple, oil, buttermilk, and vanilla in a separate large bowl. Add flour mixture to egg mixture, stirring until just combined.
Pour batter evenly into prepared muffin trays. Bake in preheated oven until a wooden pick inserted in centers of cupcakes comes out clean, about 15 minutes. Remove from oven; let cupcakes cool in trays on a wire rack 5 minutes. Remove cupcakes from trays; let cool completely on a wire rack, about 1 hour.
Beat cream cheese, powdered sugar, and yogurt with an electric mixer on high speed until smooth, about 1 minute. Spoon mixture into a piping bag; snip 1/2 inch from 1 bag corner. Pipe frosting evenly onto each cupcake. Top each cupcake with 1 carrot twist.