01 - Whisk together the flour, baking powder, and salt in a medium bowl. Set aside for later use.
02 - Beat the softened butter and granulated sugar in a large bowl until light and fluffy, approximately 2-3 minutes.
03 - Add the egg and vanilla extract to the butter mixture. Mix until thoroughly combined and smooth.
04 - Gradually incorporate the dry ingredients into the wet mixture, mixing just until the flour disappears. Avoid overmixing.
05 - Divide the dough in half. Roll each half between two sheets of parchment paper into a rectangle approximately 1/4 inch thick.
06 - Brush each rectangle with melted butter. Sprinkle the brown sugar and cinnamon mixture evenly across the surface.
07 - Starting from the long side, tightly roll each rectangle into a log. Wrap securely in plastic wrap and refrigerate for 1 hour.
08 - Preheat the oven to 350°F. Line two baking sheets with parchment paper.
09 - Slice the chilled dough logs into 1/2-inch rounds. Place on prepared baking sheets 2 inches apart. Bake for 9-11 minutes until edges are golden.
10 - Let cookies cool on baking sheets for 5 minutes, then transfer to a wire rack. Whisk powdered sugar, milk, and vanilla until smooth. Drizzle over cooled cookies.