Warm milk in a saucepan or microwave until it reaches 100-110°F. Pour into a large mixing bowl and sprinkle yeast on top. Let sit for 5–10 minutes until foamy.
Add sugar, egg, egg yolk, and melted butter to yeast mixture. Stir to combine.
Gradually add flour and salt, mixing until a soft dough forms. Knead by hand or with a dough hook for 8–10 minutes until smooth and elastic.
Transfer dough to a greased bowl, cover with a kitchen towel, and let rise in a warm place for about 1 hour or until doubled in size.
Meanwhile, prepare the filling. In a small bowl, mix softened butter, brown sugar, cinnamon, and cocoa powder until well blended.
Punch down dough and roll out on a floured surface into a 14 x 18-inch rectangle.
Spread filling evenly over dough, then sprinkle with chopped chocolate.
Starting from the long side, roll dough tightly into a log. Slice into 12 equal pieces using a serrated knife or unflavored dental floss.
Arrange rolls in a greased 9 x 13-inch baking dish. Cover and let rise again for 30–40 minutes until puffy.
Preheat oven to 350°F (175°C). Bake 22–26 minutes, until golden brown and the centers are cooked through.
While rolls cool slightly, whisk together powdered sugar, cocoa powder, milk, and vanilla until smooth. Drizzle glaze over warm rolls and serve.