Prepare the Dough. In a large bowl, combine warm milk, sugar, and yeast. Let it sit for 5 minutes until foamy. Add melted butter, eggs, salt, and flour. Mix until a soft dough forms. Knead the dough on a floured surface for 8–10 minutes until smooth and elastic. Place the dough in a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.
Make the Filling. In a small bowl, mix cocoa powder, brown sugar, and cinnamon. Spread softened butter evenly over the rolled-out dough. Sprinkle the chocolate mixture and chocolate chips on top.
Roll and Cut. Roll the dough into a rectangle, about 12x16 inches. Starting from one long side, tightly roll the dough into a log. Slice into 12 even pieces and place them in a greased baking dish.
Rise Again. Cover the rolls and let them rise for 30 minutes, or until puffed up.
Bake. Preheat the oven to 350°F. Bake the rolls for 20–25 minutes or until golden brown.
Frost and Serve. While the rolls are baking, whisk together powdered sugar, milk, and vanilla for the frosting. Drizzle over warm rolls and enjoy!