In a large bowl, mix flour, yeast, sugar, and salt. Add warm milk, melted butter, and egg. Stir until a sticky dough forms.
Knead the dough by hand or with a dough hook for 6 to 8 minutes until smooth and elastic. Place dough in a greased bowl, cover, and let rise until doubled, about 1 hour.
In a small bowl, combine brown sugar, cocoa powder, and cinnamon.
On a floured surface, roll dough to a 16x10-inch rectangle. Spread softened butter evenly over dough.
Sprinkle the brown sugar mixture evenly, then add chocolate chips and crushed peppermint candies on top.
Roll the dough tightly from the long side and slice into 12 equal rolls. Arrange rolls in a greased 9x13-inch baking dish, cover, and let rise for 30 to 40 minutes until puffy.
Preheat oven to 350°F. Bake rolls for 22 to 25 minutes until golden and cooked through.
Beat cream cheese and butter until smooth. Add powdered sugar and peppermint extract; mix well. Gradually add milk to reach desired glaze consistency.
Spread glaze over warm rolls and sprinkle with crushed peppermint bark. Serve warm.