In a small pot, melt the 1/4 cup butter and 1/2 cup whole milk. Whisk in the sugar until dissolved. Remove from heat and sprinkle the yeast over the top. Allow that to sit for 8 to 10 minutes. The yeast should appear to foam some on the surface as the mixture cools.
In a large bowl, combine the flour and egg. Pour the milk-yeast mixture into the bowl and stir until a dough ball forms. On a floured surface, knead the dough for 2-3 minutes. Place back in the bowl and cover with a clean kitchen towel. Allow to rise in a warm spot for 1 hour or until doubled in size.
Once the dough has risen, punch down and turn out onto a floured surface. Roll into a large rectangle. Smear the softened 1/4 cup butter all over the rectangle. Combine the sugar and cocoa and then sprinkle over the butter. Sprinkle on the chopped chocolate. Roll up into a long cylinder. Cut in about 8-10 rolls (if you cut slightly more or less, that's OK too). Place in a buttered pie pan or square pan.
Bake at 325°F for 30-32 minutes, until the edges begin to turn golden brown. Allow to cool while you make the glaze.
In a large bowl, whisk together the powdered sugar, cocoa, vanilla, and 3 tablespoons milk. If the mixture seems too thick, add another tablespoon of milk until you get an Elmer's Glue-like consistency (like chocolate donut glaze). Drizzle over the rolls and topped with crushed candy canes if using.
