Make the Dough: In a small bowl, mix the warm milk, yeast, and 1 tablespoon of the sugar. Let it sit for 5–10 minutes until bubbly and foamy. In a large bowl, combine the remaining sugar, egg, melted butter, and the yeast mixture. Slowly incorporate the flour and salt, mixing until a soft dough begins to form. Transfer the dough to a lightly floured surface and knead for 5 to 7 minutes, or until it becomes smooth and elastic. Place the dough in a greased bowl, cover it, and let it rise in a warm area for about an hour, or until it has doubled in size.
Prepare the Filling: In a medium bowl, combine softened butter, brown sugar, granulated sugar, cocoa powder, instant coffee powder, and cinnamon. Mix until smooth.
Assemble the Rolls: Once the dough has risen, roll it out on a floured surface into a 12x18-inch rectangle. Spread the chocolate-cinnamon filling evenly over the dough, leaving a small border around the edges. Begin at the long edge and carefully roll the dough into a tight log. Cut the log into 12 equal rolls and place them in a greased 9x13-inch baking pan.
Second Rise and Bake: Cover the rolls and let them rise for 30 minutes. Preheat your oven to 350°F (175°C). Bake the rolls for 25 to 30 minutes, or until they turn a rich golden brown. Let them cool for a few minutes as you prepare the glaze.
Make the Espresso Glaze: In a small bowl, whisk together powdered sugar, brewed coffee, vanilla extract, instant coffee powder, and milk. Adjust the consistency with additional milk if needed to make a smooth, pourable glaze.
Glaze and Serve: Drizzle the espresso glaze over the warm rolls. Serve warm and enjoy the rich chocolate, cinnamon, and coffee flavors in each bite.