Whisk the flour, sugar, and salt together in a large bowl. Set aside.

Combine the milk and butter in a heatproof bowl and heat until the butter has melted and the mixture is warm (about 110°F/43°C). Whisk in the yeast until dissolved.

Pour the milk mixture into the dry ingredients, add the egg, and stir until a soft dough forms.

Transfer dough to a floured surface. Knead for 3-5 minutes until you have a smooth ball. Place in a greased bowl, cover, and let rest for about 10 minutes.

Roll the dough into a 14x8-inch rectangle. Spread softened butter on top, sprinkle cinnamon and brown sugar, then roll into a log.

Cut into 10-12 rolls and arrange in a greased pan.

Cover the pan and let the rolls rise in a warm environment for 60-90 minutes or until double in size.

Preheat oven to 375°F (190°C) and bake for 24-27 minutes until golden brown.

In a bowl, beat cream cheese until smooth, then add butter and beat until combined. Add confectioners’ sugar and vanilla, mix until smooth.

Spread icing over warm rolls and serve immediately. Store leftovers tightly covered at room temperature for a day or in the refrigerator for up to 5 days.