In a mixing bowl, combine warm milk, sugar, and yeast. Let it sit for 5 minutes until frothy.

Add melted butter, egg, and salt to the yeast mixture. Gradually add flour, mixing until a dough forms.

Knead the dough on a floured surface for about 5 minutes until smooth. Place in a greased bowl, cover, and let rise for 1 hour.

In a small bowl, mix instant coffee, brown sugar, and cinnamon. Set aside.

Preheat the oven to 350°F (175°C). Roll out the dough on a floured surface into a rectangle.

Spread the filling evenly over the dough. Roll tightly into a log and cut into 8 equal pieces.

Place the rolls on a baking sheet lined with parchment paper. Cover and let rise for another 30 minutes.

Bake the rolls in the preheated oven for 20-25 minutes until golden brown.

While the rolls are baking, whisk together powdered sugar, milk, and vanilla to make the glaze.

Once baked, remove from the oven and drizzle the glaze over the warm rolls.