01 - In a large bowl or stand mixer, combine flour, sugar, yeast, and salt.
02 - Add lukewarm milk and eggs to dry ingredients; mix on low speed until a shaggy dough forms.
03 - Gradually add softened butter, mixing until fully incorporated and dough is smooth and elastic, about 8 to 10 minutes.
04 - Cover the dough and let it rise in a warm place until doubled in size, approximately 1 to 1.5 hours.
05 - Beat together softened butter, brown sugar, cocoa powder, espresso powder, and peppermint extract until smooth.
06 - Punch down the dough and roll out on a lightly floured surface into a 12 by 18-inch rectangle.
07 - Spread the filling evenly over the dough and sprinkle with mini chocolate chips.
08 - Roll the dough tightly from the long side into a log and slice into 12 equal pieces.
09 - Arrange buns cut-side up in a buttered 9 by 13-inch baking dish, cover, and let rise for 30 to 45 minutes until puffy.
10 - Preheat the oven to 350°F (175°C).
11 - Bake for 25 minutes until golden and set.
12 - While baking, mix granulated sugar and peppermint extract; stir in crushed candy canes.
13 - Whisk powdered sugar, milk, and peppermint extract until smooth for an optional glaze.
14 - Cool buns slightly, sprinkle with peppermint sugar, drizzle glaze if desired, and serve warm.