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 6 tablespoons of butter until warm and the butter is mostly melted, about 45 seconds.

Pour the milk mixture into the flour mixture. Add the egg and beat on low speed until combined. Gradually increase to high speed 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 of the bowl as needed. Add the remaining 1 cup of flour and continue kneading until the dough pulls away from the sides of the bowl and 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 and cover with a dish towel or plastic wrap. Let rise in a warm place until doubled in size, about 1 hour.

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

Turn the risen dough onto a well-floured surface and roll it into a 12-inch by 18-inch rectangle.

Spread 1/4 cup of butter over the dough, then sprinkle the brown sugar mixture on top and spread it into the butter.

Roll the dough into a tight log from the 18-inch side closest to you, seal the seam, and cut into 12 even rolls.

Place the rolls in a 9 x 13-inch pan lined with parchment paper and cover. Allow to rise in a warm place until doubled, about 1 hour.

Preheat the oven to 350°F. Bake the rolls until golden brown, about 30 minutes.

Allow to cool on a wire rack for about 15 minutes while preparing the frosting.

In a stand mixer, combine the cream cheese, butter, powdered sugar, 2 tablespoons of milk, vanilla, and a pinch of salt. Beat on low speed until combined, then increase to medium-high and beat until light and fluffy, about 1 minute. Add additional milk if needed for consistency.

Spread the frosting evenly over the slightly warm rolls.