In a small bowl, combine warm milk and yeast. Allow it to sit for 5-10 minutes until it's frothy.

In a large mixing bowl, combine flour, sugar, salt, and melted butter. Add the yeast mixture and egg, mixing until it forms a soft dough.

Turn the dough onto a floured surface and knead for about 5 minutes, or until it’s smooth and elastic.

Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm area for about 1 hour, or until doubled in size.

Combine brown sugar and cinnamon in a small bowl. Set aside.

Once risen, punch the dough down and roll it out into a rectangle, about 1/4-inch thick.

Slather the rolled-out dough with softened butter, then sprinkle the cinnamon-sugar mixture over the top.

Starting from one edge, carefully roll the dough into a log. Slice into 12 equal pieces.

Place the rolls in a greased baking dish. Cover and let rise for another 30 minutes. Preheat the oven to 350°F (175°C) while they rise, then bake for 20-25 minutes until golden brown.

While the rolls are baking, whisk together powdered sugar, milk, and vanilla until smooth. Drizzle over warm rolls once they’re out of the oven.