In a large mixing bowl, combine the warm milk, granulated sugar, and yeast. Let it sit for about 5 minutes until frothy.
Add the melted butter and egg to the yeast mixture, and stir until well combined.
Gradually add the flour and salt, mixing until a dough forms. Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
Once risen, punch down the dough and roll it out on a floured surface into a rectangle (about 12x18 inches).
Spread the softened butter over the dough, then sprinkle the brown sugar and cinnamon evenly on top.
Starting from one long edge, roll the dough tightly into a log. Cut the log into 12 equal pieces.
Place the rolls in a greased 9x13 inch baking dish. Cover and let them rise for another 30 minutes.
Preheat the oven to 350°F. Bake the rolls for 20-25 minutes, or until golden brown.
While the rolls are baking, prepare the glaze by mixing powdered sugar with 1-2 tablespoons of milk until smooth.
Drizzle the glaze over the warm rolls before serving.