Warm the milk in the microwave or on the stove until just warm to the touch (about 110°F / 43°C). Add yeast and sugar, stir, and let sit for 5–10 minutes until foamy.

In a large bowl, combine the melted butter, egg, and salt. Add the yeast mixture and mix together.

Gradually add flour, one cup at a time, mixing until a soft dough forms. Knead for about 5 minutes until smooth and elastic.

Place the dough in a greased bowl, cover, and let rise in a warm spot for 1 hour or until doubled in size.

In a small bowl, mix together the brown sugar and cinnamon for the filling.

Roll out the dough on a floured surface into a rectangle about 1/4 inch thick. Spread the softened butter evenly over the dough, then sprinkle with the cinnamon sugar mixture.

Roll up the dough tightly into a log and slice into 12 equal pieces.

Place the rolls in a greased 9x13 inch baking dish. Cover and let rise again for 30 minutes.

Preheat oven to 350°F (175°C). Bake the rolls for 20–25 minutes or until golden brown.

For the icing, beat together cream cheese, butter, powdered sugar, and vanilla until smooth. Spread over warm buns before serving.