• In a large bowl, combine 3 cups of flour, sugar, instant yeast, and salt. Whisk these ingredients together and set the bowl aside.
• In a medium bowl, mix the warm water, whole milk, and sliced unsalted butter. Microwave gently until the butter melts and becomes warm to touch.
• Whisk the large egg into the warm liquid mixture until fully combined.
• Pour the warm wet ingredients over the flour mixture. Stir together until a thick dough forms, ensuring no dry flour remains.
• Add the remaining flour a little at a time until the dough is smooth and slightly tacky. Knead the dough on a floured surface until elastic, then cover and let rest for 20 minutes.

Rolling and Shaping

• Roll the dough into a 14x10 inch rectangle.
• Spread the very soft unsalted butter evenly over the rolled-out dough. Sprinkle the brown sugar and ground cinnamon mixture on top of the butter.
• Starting from one long side, roll the dough into a log shape. Cut the log into 12 even rolls using a sharp knife or kitchen string.
• Place the rolls cut side up in a greased baking dish. Cover with a kitchen towel and let rise for 45 minutes in a warm spot.
• While the rolls rise, preheat your oven to 350°F (175°C).

Baking

• Once the rolls have risen, bake them in the preheated oven for 25-30 minutes until golden brown.

Icing

• In a mixing bowl, combine the cream cheese, softened butter, powdered sugar, and vanilla extract. Mix until smooth and creamy.
• Spread the warm icing on top of the rolls as soon as they come out of the oven.