In a bowl, combine warm milk and yeast; let it sit for 5 minutes.
Add melted butter, sugar, and eggs to the yeast mixture, mixing well.
Gradually add flour and salt, stirring until a dough forms.
Knead the dough on a floured surface for about 10 minutes until smooth.
Place the dough in a greased bowl, cover, and let it rise for 1 hour.
Preheat the oven to 350°F (175°C).
Roll the dough into a rectangle, about 1/4 inch thick.
Spread softened butter over the dough, then sprinkle cinnamon and brown sugar evenly.
Roll the dough tightly into a log and cut into 12 equal pieces.
Place the rolls in a greased baking dish and let rise for another 30 minutes.
Bake for 25 minutes until golden brown.
Mix powdered sugar with milk to create icing, and drizzle over warm buns.