In a large mixing bowl, combine the flour, granulated sugar, salt, and instant yeast. Mix well.

In a separate bowl, whisk together the warm milk, melted butter, egg, and vanilla extract.

Pour the wet ingredients into the dry ingredients and mix until a dough forms. Knead for about 5 minutes until smooth.

Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.

While the dough is rising, prepare the coffee filling by mixing the cocoa powder, granulated sugar, cooled brewed coffee, cinnamon, and softened butter in a bowl until smooth.

After the dough has risen, punch it down and roll it out on a floured surface into a rectangle about 1/4 inch thick.

Spread the coffee filling evenly over the dough. Roll the dough tightly into a log and cut it into 12 equal pieces.

Place the dough pieces in a greased baking dish, cover, and let them rise for another 30 minutes.

Preheat the oven to 350°F. Bake the buns for 20-25 minutes or until golden brown.

While the buns are baking, prepare the topping by whisking together the powdered sugar, brewed coffee, and vanilla extract until smooth.

Once the buns are done, remove them from the oven and drizzle the coffee topping over the warm buns. Serve warm.