Warm the milk and butter in the microwave till butter is melted. Allow to cool till lukewarm. Stir in sugar and yeast and set aside.
In a large bowl, add the flour and salt. Whisk together. Add in the beaten egg and pour the milk mixture. Bring the dough together.
Add extra flour little by little till you have a slightly sticky pliable dough. I added extra 1/4 cup. Knead for 10-12 minutes. Shape the dough and keep in an oiled bowl for proofing till double for an hour.
After an hour, punch down the dough. Flatten it into a rectangle for around 10 inch to 7 inch.
Brush the softened butter all over. Whisk the brown sugar and cinnamon well, and sprinkle on top of the butter.
Slowly roll tightly and fold. Cut into 8 equal pieces. Arrange in a greased small round tray, or in a fluted pan. Cover and keep for 45 minutes.
Preheat oven to 180 degrees. Bake for 25 minutes.
Meanwhile, whisk together the ingredients for the topping till smooth. Drizzle over warm buns lavishly. Serve warm and enjoy.
If having next day, microwave the bun for 20-30 seconds and enjoy them.
Notes
To make the recipe eggless, you can simply skip the egg altogether or add 2 tbsp of yogurt or cream instead for extra softness.