In a mixing bowl, combine warm milk, melted butter, and sugar. Stir in the yeast and let it sit for 5 minutes until foamy.

Add the egg, salt, and flour gradually, 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 or until doubled in size.

In a small bowl, mix together brown sugar, ground coffee, cinnamon, and softened butter until well combined.

Preheat the oven to 375°F (190°C).

Roll out the dough on a floured surface into a rectangle about 1/4 inch thick.

Spread the filling evenly over the dough, then roll it up tightly from the long side.

Cut the roll into 8 equal pieces and place them on a greased baking sheet.

Cover and let rise for another 30 minutes.

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

While baking, prepare the glaze by whisking together powdered sugar, milk, and vanilla extract.

Once baked, drizzle the glaze over the warm rolls before serving.