In a large bowl, whisk together flour, sugar, yeast, and salt.

In a separate microwave-safe bowl, heat milk until warm (105-115°F/40-46°C), then stir in melted butter and egg.

Pour the wet ingredients into the dry ingredients and mix until a shaggy dough forms, then knead on a lightly floured surface for 5-7 minutes until smooth and elastic.

Place the dough in a lightly oiled bowl, cover with plastic wrap, and let rise in a warm place for 1-1.5 hours, or until doubled in size.

While the dough rises, combine brown sugar and cinnamon in a small bowl.

Once the dough has risen, punch it down and roll it into a 12x8 inch rectangle on a lightly floured surface.

Spread the softened butter evenly over the dough, leaving a small border, then sprinkle the cinnamon-sugar mixture over the butter.

Starting from a long side, tightly roll up the dough and pinch the seam to seal it.

Cut the log into 4 equal pieces using a sharp knife or dental floss.

Preheat your oven to 375°F (190°C) and lightly grease a 8x8 inch baking dish.

Place the cinnamon rolls, cut-side up, in the prepared baking dish, leaving some space between them.

Cover the dish with plastic wrap or a clean kitchen towel and let them rise again for 20-30 minutes, or until noticeably puffy.

Bake for 18-22 minutes, or until golden brown and cooked through.

While the cinnamon rolls cool slightly, beat together softened cream cheese, powdered sugar, softened butter, vanilla extract, and milk in a medium bowl until smooth and creamy.

Spread the frosting generously over the warm cinnamon rolls and serve immediately.