In a large mixing bowl, whisk together 1 cup of flour, cocoa powder, granulated sugar, instant coffee granules, salt, and active dry yeast until well combined.
In a separate bowl, combine the warm milk, melted butter, and beaten egg. Whisk until the mixture is smooth and well combined.
Pour the wet ingredient mixture into the dry ingredients, stirring continuously with a wooden spoon or spatula until the dough begins to come together.
Gradually add the remaining flour, a little at a time, mixing until a soft dough forms. Transfer the dough to a lightly floured surface and knead for about 5 minutes, or until it becomes smooth and elastic.
Shape the kneaded dough into a ball and place it in a greased bowl. Cover the bowl with a clean kitchen towel and let it rise in a warm, draft-free area for about 1 hour, or until it has doubled in size.
Once the dough has risen, gently punch it down to release excess air. Roll it out using a rolling pin into a rectangle approximately 12x8 inches.
In a small mixing bowl, combine the brown sugar and ground cinnamon. Sprinkle this mixture evenly over the surface of the rolled-out dough, then scatter the chocolate chips on top.
Starting from one long edge, tightly roll the dough into a log, ensuring a snug fit. Slice the rolled dough into 12 equal pieces, each about 1 inch thick.
Arrange the rolls in a greased baking dish, making sure they are close but not touching. Cover with a towel and allow them to rise again for about 30 minutes.
Preheat your oven to 350°F. Once the rolls have puffed up, place them in the oven and bake for 20-25 minutes or until they are beautifully golden brown on top.
While the rolls are baking, prepare the icing by combining sifted powdered sugar, brewed coffee, and milk in a small bowl. Whisk until the mixture is smooth and creamy, adjusting the consistency with more milk if necessary.
After removing the rolls from the oven, allow them to cool in the pan for just a few minutes before drizzling the icing generously over them.