Preheat your oven to 375°F (190°C) and grease a 9-inch round cake pan.
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt.
In a separate bowl, combine the milk, melted butter, and egg. Mix well.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
On a lightly floured surface, roll out the dough into a rectangle about 1/4 inch thick.
Spread the softened butter over the dough, then sprinkle the brown sugar and cinnamon evenly on top.
Starting from one long edge, roll the dough tightly into a log. Pinch the seam to seal.
Cut the log into 8 equal pieces and place them in the prepared cake pan, cut side up.
Bake for 20-25 minutes, or until golden brown. Let cool for 5 minutes in the pan.
While the rolls are cooling, whisk together the powdered sugar and milk to make the icing.
Drizzle the icing over the warm rolls before serving.