Stir together the warm water and yeast. Let sit for 5–10 minutes, or until the mixture becomes foamy.
In the bowl of a stand mixer fitted with the paddle attachment, combine the milk, melted butter, brown sugar, granulated sugar, salt, egg, and yeast mixture.
Gradually add 3 cups flour, about 1 cup at a time, mixing on low speed until a soft dough forms. Add additional flour as needed, up to 3½ cups total.
Transfer the dough to a lightly greased bowl and turn once to coat.
Cover tightly with plastic wrap and let rise in a warm place for 1–1½ hours, or until doubled in size.
Turn the dough onto a lightly floured surface and knead for 1–2 minutes.
Roll the dough into approximately a 15x24-inch rectangle.
For the Filling:
In a small bowl, stir together the softened butter, brown sugar, cinnamon, and cocoa powder until combined.
Spread the filling evenly over the dough.
Sprinkle the finely chopped semi-sweet chocolate evenly over the filling and gently press it into the dough.
Starting with a long side, tightly roll the dough into a log.
Cut the log into 12 equal rolls using unflavored dental floss or a serrated knife.
Arrange the rolls in a lightly greased 9x13-inch baking dish.
Cover and let rise for 30–60 minutes, or until noticeably puffy.
Preheat the oven to 350°F.
Bake for 20–25 minutes, or until the rolls are lightly golden and cooked through.
Let the rolls cool for about 15–20 minutes before glazing.
For the Glaze:
Beat the softened cream cheese, powdered sugar, vanilla extract, cocoa powder, and 2 tablespoons milk until smooth and creamy.
Add additional milk, 1 tablespoon at a time, if needed to reach your desired consistency.
Spread the glaze over the warm chocolate cinnamon rolls and serve.
Notes
Add only as much of the additional ½ cup flour as needed to create a soft dough. Too much flour can make the rolls dense.For 12 evenly sized cinnamon rolls from a 15x24-inch rectangle, rolling from a long side generally produces more manageable rolls.Store leftovers in an airtight container in the refrigerator for up to 1 week. Reheat individual rolls in the microwave for about 20–30 seconds before serving.