In a large mixing bowl, combine 2 cups of flour, instant yeast, sugar, and salt.
Add the warm milk, melted butter, and egg. Mix until smooth.
Gradually add the remaining flour until a soft dough forms.
Knead the dough for 5 minutes until smooth and elastic.
Cover the dough with a towel and let it rest for 10 minutes.
In a small bowl, mix the softened butter, brown sugar, and cinnamon until smooth.
Roll out the dough into a 12×18-inch rectangle on a floured surface.
Spread the cinnamon filling evenly over the dough.
Roll up the dough tightly from the long side and cut into 12 even slices.
Place the slices in a greased 9×13-inch baking dish.
Cover loosely with a towel and let them rest for 10 minutes while preheating the oven to 375°F (190°C).
Bake for 20–25 minutes, or until golden brown.
While the rolls bake, whisk together the powdered sugar, milk, and vanilla extract until smooth.
Drizzle the glaze over warm rolls and serve immediately.