- STIR flour with baking powder and salt in a medium bowl. Set aside.
- BEAT butter with granulated sugar and 1/2 cup brown sugar in a large bowl, using an electric mixer on medium-high, until fluffy. Beat in egg and vanilla. Gradually beat in flour mixture, just until combined. Gather into a ball. Divide dough in half. Roll each portion into a 8 × 8-in. square. Combine remaining 1/4 cup brown sugar and ground cinnamon together in a small bowl. Sprinkle half of cinnamon mixture on each square. Spread to cover cookie dough, stopping 1/8 in. from the edge. Brush edge with water, then roll into a log. Press seam gently. Chill until firm, 1 to 1 1/2 hours.
- POSITION racks in top and bottom thirds of oven. Preheat to 350F. Line 2 baking sheets with parchment.
- SLICE cookies into 1/4-inch rounds and arrange 1 inch apart on prepared sheets. Bake in top and bottom thirds of oven, switching halfway through, until cookies are golden, 10 to 12 min. Let cookies cool on sheets for 1 min, then transfer to a wire rack to cool completely. Repeat with remaining dough. Whisk icing sugar with milk until smooth. Spoon into a zip-top freezer bag. Snip off 2 mm from a corner of bag. Drizzle icing over cookies. Cookies will keep well, stored in an airtight container at room temperature, up to 5 days.
Weekend baking: How to make cinnamon buns