01 - Whisk together flour, baking powder, and salt in a medium bowl until thoroughly combined. Set mixture aside for later use.
02 - Beat softened butter and granulated sugar in a large bowl until light and fluffy, approximately 2–3 minutes. Scrape down sides of bowl to ensure even mixing.
03 - Incorporate egg and vanilla extract into the butter mixture, beating until fully blended and smooth.
04 - Gradually mix in dry ingredients on low speed until a soft, cohesive dough forms. Avoid overmixing to prevent tough cookies.
05 - Divide dough in half. Roll each half between parchment sheets into a 1/4-inch thick rectangle (approximately 9x7 inches). Brush with melted butter and sprinkle evenly with brown sugar-cinnamon mixture.
06 - Starting from a long side, roll each rectangle tightly into a log. Wrap in parchment paper and refrigerate for minimum 30 minutes until firm enough to slice cleanly.
07 - Preheat oven to 350°F. Line baking sheets with parchment paper and set aside.
08 - Cut chilled dough logs into 1/2-inch thick rounds. Place on prepared baking sheets, leaving 2 inches of space between cookies to allow for spreading.
09 - Bake for 10–12 minutes until edges are lightly golden. Centers should appear slightly underbaked for optimal texture. Transfer to wire rack to cool completely.
10 - Whisk powdered sugar, 1 tablespoon milk, and vanilla extract until smooth. Add additional milk 1/2 teaspoon at a time to achieve drizzling consistency.
11 - Drizzle glaze generously over completely cooled cookies. Allow glaze to set for 10–15 minutes before serving or storing.