Heat oven to 350°. Coat the cups of 2 mini muffin pans with nonstick cooking spray (22 per batch).
In a medium bowl, whisk cake flour, cocoa powder, baking powder, baking soda and salt. In a large bowl, beat softened butter and brown sugar until smooth. Add egg and beat until creamy, 2 minutes. On low speed, beat in half the flour mixture, then the buttermilk, followed by remaining flour mixture. Stir in vanilla. Divide batter into prepared pans, about 1 tbsp batter per cup.
Bake at 350° for 12 to 14 minutes. Cool 10 minutes in pans on wire racks, then remove directly to racks to cool. Repeat with a second batch of 22.
While duffins cool, melt butter in microwave, 30 seconds. Combine granulated sugar and cocoa in a small bowl. Dip duffin tops in melted butter, followed by cocoa sugar. Serve slightly warm.