In a large bowl, mix together the flour, yeast, sugar, and salt. Pour in the warm milk, melted butter, and egg. Stir until a sticky dough forms, and knead for 6–8 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise for 1 hour or until doubled in size.

In a small bowl, whisk together brown sugar, cocoa powder, and ground cinnamon.

On a lightly floured surface, roll your dough into a 16×10-inch rectangle. Spread the softened butter over the dough and sprinkle it evenly with the brown sugar-cocoa mixture, followed by the chocolate chips and crushed peppermint candies.

Tightly roll up the dough from the long side and slice into 12 equal rolls. Place them in a greased 9×13-inch baking dish, cover, and let rise for another 30–40 minutes until they're puffy.

Preheat your oven to 350°F (175°C). Bake the rolls for 22–25 minutes, or until they are golden brown.

Beat the cream cheese and softened butter together until smooth. Gradually mix in the powdered sugar and peppermint extract. Add milk until the desired consistency is reached.

Optional: Sprinkle additional crushed peppermint bark on top for a festive finish.