Whisk together the flour, baking powder, and salt in a medium bowl and set aside.
Cream the softened butter and sugar on high speed until fluffy, then blend in the egg and vanilla until smooth.
Scrape the bowl, then mix in the dry ingredients on low speed until a soft dough forms, adding a small amount of flour only if needed for easier rolling.
Divide the dough into two portions, rolling each into a 9×7-inch rectangle on a lightly floured mat. Spread melted butter over each sheet, then coat evenly with the cinnamon-sugar mixture.
Roll each rectangle tightly into a log, smoothing any small cracks, then chill the logs for at least 2 hours.
Heat the oven to 350°F (177°C) and line baking sheets with parchment or silicone mats.
Slice the chilled logs into ½-inch rounds and arrange them on the baking sheets with space between each.
Bake for 10–11 minutes until edges are lightly golden, then cool briefly on the sheet before transferring to a rack.
Whisk the icing ingredients together, then drizzle over the cooled cookies.
Notes
Warm notes of cinnamon and vanilla make these cookies feel like a tiny celebration. Perfect for gifting, sharing, or keeping for a quiet moment of joy.