Make the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan or two 24-cup mini muffin pans with paper liners; lightly spray the liners with cooking spray. Soak the prunes in a bowl with 3/4 cup hot water until softened, about 10 minutes. Pour into a blender and puree until smooth.
Whisk the all-purpose flour, whole-wheat flour, cocoa powder, baking powder, baking soda, salt and cinnamon in a large bowl. In another bowl, whisk the prune puree, brown sugar, eggs, yogurt, vegetable oil and vanilla. Fold the wet ingredients into the dry ingredients until just combined (it's fine if there are a few lumps).
Divide the batter among the muffin cups, filling each three-quarters of the way. Bake until a toothpick comes out clean, 18 to 20 minutes for standard-size cupcakes, or 12 to 14 minutes for minis. Transfer to a rack and let cool in the pan, 10 minutes, then remove from the pan to cool completely.
Make the frosting: Whisk the egg whites, granulated sugar, cream of tartar and salt in a heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water) until the sugar dissolves, 1 to 2 minutes. Remove the bowl from the pan. Transfer the egg white mixture to a stand mixer fitted with the whisk attachment; beat on medium-high speed until stiff peaks form, 3 to 5 minutes. Sift in the cocoa powder and add the vanilla and orange zest; beat to combine. Spread the frosting on the cupcakes.