In a bowl, warm the milk until lukewarm and dissolve the yeast in it.
Add sugar, butter, and egg to the mixture and stir until combined.
Gradually mix in flour and salt until a dough begins to form.
Knead the dough on a floured surface for about 5-7 minutes until smooth.
Place the dough in a greased bowl, cover, and let rise for 1 hour until doubled in size.
Preheat the oven to 350°F (175°C).
Roll out the dough into a rectangle about 1/4 inch thick.
Spread softened butter, brown sugar, and cinnamon evenly over the dough.
Roll the dough tightly into a log and slice into 12 equal pieces.
Place the slices in a greased baking dish and let rise for another 30 minutes.
Bake for 25-30 minutes until golden brown and cooked through.
Mix powdered sugar and milk to create icing, drizzle over warm buns.