Step 1: Prepare the Dough

1. In a stand mixer fitted with the whisk attachment, combine 2 cups of bread flour, granulated sugar, instant yeast, and salt.
2. In a microwave-safe bowl, warm the milk and butter for about 45 seconds, until the butter is mostly melted and the mixture is warm but not hot.
3. Pour the milk mixture into the flour mixture and add the egg.
4. Beat on low speed until combined, then increase to high speed and mix for 2 minutes.

Step 2: Knead the Dough

1. Replace the whisk attachment with the dough hook.
2. Add 1½ cups of flour and knead on low speed until combined.
3. Add the remaining 1 cup of flour and continue kneading until the dough pulls away from the sides of the bowl.
4. Increase to medium-low speed and knead for approximately 10 minutes until the dough becomes smooth and elastic.
5. Check the dough by stretching a small piece between your fingers. It should become thin enough to let light through without tearing.

Step 3: First Rise

1. Transfer the dough to a lightly oiled bowl.
2. Cover with a clean kitchen towel or plastic wrap.
3. Let rise in a warm place for approximately 1 hour, or until doubled in size.

Step 4: Make the Cinnamon Filling

1. In a medium bowl, combine softened butter, brown sugar, cinnamon, and salt.
2. Mix with a spatula until a smooth paste forms.

Step 5: Shape the Cinnamon Rolls

1. Transfer the risen dough to a well-floured surface.
2. Roll it into a rectangle measuring approximately 12 × 18 inches.
3. Spread the cinnamon filling evenly over the entire surface.
4. Starting from the longer 18-inch side closest to you, roll the dough tightly into a log.
5. Seal the outside seam by gently pressing the dough together.
6. Cut into 12 equal rolls using a sharp knife or unflavored dental floss.
7. Arrange the rolls in a parchment-lined 9 × 13-inch baking pan.

Step 6: Second Rise and Bake

1. Cover the pan with a kitchen towel or plastic wrap.
2. Let the rolls rise in a warm place for approximately 1 hour, or until doubled in size.
3. Preheat the oven to 350°F (175°C).
4. Bake for approximately 30 minutes, until the rolls are golden brown.
5. Transfer the pan to a cooling rack and allow the rolls to cool slightly for about 15 minutes.

Step 7: Prepare the Cream Cheese Frosting

1. In a stand mixer, combine cream cheese, softened butter, powdered sugar, milk, vanilla extract, and salt.
2. Beat on low speed until combined.
3. Increase to medium-high speed and whip for approximately 1 minute until light and fluffy.
4. If the frosting is too thick, add another tablespoon of milk.
5. Spread the frosting evenly over the slightly warm cinnamon rolls.
6. Serve warm and enjoy!