To the bowl of a stand mixer add the flour, yeast, sugar and salt and mix on low speed.

Add the butter and egg to the bowl. Then slowly pour in the milk. Increase the speed to medium and mix for 10 minutes.

Transfer the dough to a greased bowl, cover, and let rise for about 2 hours or until doubled in size.

Punch down the dough and roll it out into a large rectangle. Spread the softened butter for the filling evenly over the dough.

Mix the brown sugar and cinnamon together and sprinkle it evenly over the buttered dough.

Carefully roll up the dough tightly. Cut it into 12 even pieces. Place the rolls on a parchment paper lined baking sheet and cover. Let rise for 1 hour.

Bake the rolls in a preheated oven at 350 for 20 minutes.

While the rolls bake, add the butter, powdered sugar, vanilla, and milk to a clean stand mixer bowl. Mix until smooth and creamy.

Let the cinnamon rolls rest for 5 to 10 minutes before slathering them with the icing.