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 and mix 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 softened butter, brown sugar, and cinnamon until well combined.

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, then roll it tightly into a log.

Cut the log into 8 equal pieces and place them on a greased baking sheet. Let them rise for another 30 minutes.

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

Remove from the oven and let cool slightly before glazing.

In a bowl, whisk together powdered sugar, coffee, and vanilla until smooth.

Drizzle the glaze over the warm rolls before serving.