In a stand mixer fitted with the whisk attachment, mix 2 cups of the flour with the granulated sugar, yeast, and salt on low speed until combined.

In a microwave-safe bowl, microwave the milk and butter until warm to touch and butter is mostly melted, about 45 seconds.

Pour the milk mixture into the flour mixture. Add in the egg. Beat everything together on low speed until combined, then increase to high and beat for 2 minutes.

Change to the dough hook attachment. Add 1 ½ cups of flour and knead on low speed until combined. Scrape down the sides, add remaining flour until it forms a ball.

Increase to medium-low speed and knead until the dough is smooth and supple, about 10 minutes.

Transfer the dough to a lightly-oiled bowl, cover, and let rise in a warm place until doubled in size, about 1 hour.

In a small bowl, combine brown sugar, cinnamon and salt. Stir to combine.

Turn the dough onto a floured surface, roll into a 12-inch by 18-inch rectangle.

Spread the butter, sprinkle the brown sugar mixture on top and spread it into the butter.

Roll the dough tightly from the wide side and cut into 12 even rolls.

Place rolls in a 9 x 13-inch pan lined with parchment paper, cover and let rise until doubled in size, about 1 hour.

Preheat the oven to 350°F, remove cover and bake rolls until golden brown, about 30 minutes.

Cool the baked rolls on a wire rack for about 15 minutes.

In a stand mixer fitted with the whisk attachment, combine cream cheese, butter, powdered sugar, milk, vanilla, and salt. Beat until light and fluffy.

Spread the icing evenly over the slightly warm rolls.