Preheat and Prepare: Preheat your oven to 375°F (190°C). Lightly grease a 9-inch round or square baking dish.
Mix the Dough: In a large bowl, whisk together flour, sugar, baking powder, and salt. Add milk, melted butter, and the egg, mixing until a soft dough forms.
Knead and Roll: Transfer the dough to a floured surface and knead gently for 1–2 minutes. Roll it into a 12x10-inch rectangle.
Spread and Fill: Spread the softened butter evenly over the dough. Sprinkle with brown sugar and cinnamon mixture, covering the surface.
Roll and Slice: Roll the dough tightly from one long side to the other, forming a log. Use dental floss or a sharp knife to cut the log into 9–12 equal pieces.
Arrange and Bake: Place the rolls cut-side up in the prepared baking dish, leaving a little space between each. Bake for 20–25 minutes, or until golden brown.
Prepare the Icing: While the rolls bake, beat cream cheese and butter together until smooth. Add powdered sugar, vanilla extract, and milk, mixing until creamy.
Ice and Serve: Let the rolls cool slightly before spreading the cream cheese icing generously on top. Serve warm and enjoy!