Step 1: Prepare the Dough

1. In a small bowl, mix warm milk, sugar, and yeast. Let it sit for 5-10 minutes until foamy.
2. In a large bowl, combine flour and salt.
3. Add the yeast mixture, egg, and softened butter, then knead the dough for 10 minutes until smooth and elastic.
4. Cover with a damp cloth and let it rise for 1-2 hours until doubled in size.

Step 2: Shape the Buns

1. Punch down the risen dough and divide it into 8 equal pieces.
2. Flatten each piece, place a cube of chilled butter in the center, and seal the dough tightly around it.
3. Place the shaped buns on a baking tray lined with parchment paper.
4. Cover and let them rise again for 30 minutes.

Step 3: Prepare the Coffee Topping

1. In a bowl, beat softened butter and powdered sugar until light and fluffy.
2. Add the egg and mix well.
3. Stir in the brewed coffee and cocoa powder.
4. Gradually fold in the flour, mixing until smooth.
5. Transfer the topping mixture into a piping bag.

Step 4: Apply the Coffee Topping

1. Preheat your oven to 375°F (190°C).
2. Pipe the coffee topping in a spiral motion over each bun, covering the top surface.

Step 5: Bake and Serve

1. Bake for 15-18 minutes until the topping is crisp and the buns are golden brown.
2. Let the buns cool slightly before serving warm with a cup of coffee or tea.