Preheat the oven to 400°F (200°C). Brush an 8-inch square baking dish with 1 tablespoon of the melted butter.

To make the dough: Whisk flour, white sugar, baking powder, and salt in a large bowl. Work 3 tablespoons softened butter into the flour mixture until butter is lentil-sized.

Pour milk into the flour-butter mixture and stir with a rubber spatula until a soft dough forms.

Turn dough out onto a well-floured surface. Roll into a 10-inch square. Brush surface with remaining 2 tablespoons melted butter.

To make the filling: Mix white sugar, brown sugar, and cinnamon. Sprinkle 1 tablespoon of this mix in the prepared dish and spread the remaining mix over the dough.

Roll the dough into a log and cut into 9 rolls (1-inch wide). Place rolls cut-side up in the baking dish.

Bake in the preheated oven for 20 to 25 minutes, until puffed and lightly golden.

To make frosting: Beat confectioners’ sugar, cream cheese, butter, and vanilla extract until smooth.