In a small bowl, combine lukewarm milk and active dry yeast. Let it sit for 5 minutes until frothy.

In a large bowl, whisk together flour, sugar, and salt. Add melted butter, yeast mixture, and egg. Stir until a rough dough forms.

Knead the dough on a floured surface for 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let it rise for 1 hour.

Roll the dough into a 16x12 inch rectangle on a floured surface.

Spread softened butter over the dough, mix brown sugar and cinnamon, then sprinkle it evenly over the buttered surface.

Roll the dough tightly into a log from the long side, then slice into 12 equal pieces.

Place the rolls in a greased baking dish, cover, and let rise for another 30-45 minutes.

Preheat the oven to 350°F (175°C).

Bake the rolls for 22-25 minutes until golden brown.

Whisk together powdered sugar, milk, and vanilla extract for the glaze. Drizzle over the warm buns.