In a large mixing bowl, whisk together 2 1/2 cups of all-purpose flour, granulated sugar, instant yeast, and salt.

In a separate microwave-safe bowl, warm the milk for 30-45 seconds until it reaches 105-115°F. Add the melted butter and egg to the warm milk, whisking until combined.

Pour the wet ingredients into the dry ingredients. Stir with a wooden spoon or spatula until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic. Add small amounts of flour if the dough is too sticky (up to 1/2 cup extra).

Lightly grease the mixing bowl, place the dough back in, turn to coat. Cover the bowl with plastic wrap or a clean kitchen towel. Let rise in a warm place for 15-20 minutes, or until doubled in size. (Preheat oven to 375°F / 190°C during this time and grease a 9x13 inch baking dish.)

While the dough is rising, prepare the filling: In a small bowl, combine the softened butter, brown sugar, and ground cinnamon. Mix until well combined and paste-like.

Once the dough has risen, punch it down gently. On a lightly floured surface, roll the dough into a large rectangle, approximately 12x18 inches.

Spread the cinnamon-sugar filling evenly over the entire surface of the dough, leaving a small border (about 1/2 inch) on one long edge.

Starting from the long edge opposite the border, tightly roll the dough into a log. Pinch the seam to seal.

Using a sharp knife or unflavored dental floss, cut the log into 12 even slices (about 1.5 inches thick).

Arrange the cut rolls in the prepared 9x13 inch baking dish. Cover loosely with plastic wrap or a kitchen towel and let rise for another 10 minutes while the oven finishes preheating.

Bake the cinnamon rolls in the preheated oven for 18-22 minutes, or until golden brown on top and cooked through.

While the rolls are baking, prepare the cream cheese icing: In a medium bowl, whisk together the powdered sugar, softened cream cheese, milk, and vanilla extract until smooth and creamy. If the icing is too thick, add a few more drops of milk until desired consistency is reached.

Once the cinnamon rolls are out of the oven, let them cool in the pan for 5-10 minutes. Drizzle generously with the cream cheese icing while still warm. Serve immediately and enjoy!