Cream together butter, granulated sugar, and brown sugar until light and fluffy. Add eggs and vanilla, mixing well. Gradually incorporate flour and baking powder until a smooth dough forms.

Divide the dough into two disks, wrap in plastic wrap, and refrigerate for at least 1 hour.

Roll one disk of dough to 1/4 inch thick, brush with melted butter, and sprinkle with cinnamon and sugar. Roll tightly into a log, wrap in plastic wrap, and refrigerate for 30 minutes.

Preheat oven to 350°F (175°C). Slice the dough log into 1/2 inch rounds and bake on a parchment-lined baking sheet for 12-15 minutes.

Whisk together powdered sugar and milk until smooth. Adjust consistency as needed.

Cool cookies slightly, then drizzle the icing over each cookie.

Store cookies in an airtight container for up to 1 week at room temperature.