Beat the butter and sugar together in a large mixing bowl until light and fluffy
Whip in the egg and vanilla.
Stir in the flour, baking powder, and salt, mixing until a soft dough forms.
Divide the dough in half.
Roll each portion into a 10x12-inch rectangle on a lightly floured surface.
Blend the softened butter, brown sugar, and cinnamon together in a small bowl.
Distribute the mixture evenly between each rectangle of dough. Be sure to spread it out in an even layer.
Starting from the long side, roll each rectangle tightly into a log.
Wrap the logs in plastic wrap and refrigerate for at least 1 hour.
Preheat the oven to 350°F. Line baking sheets with parchment paper.
Slice the chilled logs into ¼-inch thick rounds and place them 2 inches apart on the prepared baking sheets.
Bake for 10-12 minutes or until the edges are just beginning to turn golden.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.
Whisk the confectioner’s sugar, milk, and vanilla together in a small bowl until smooth.
Drizzle the glaze over the cooled cookies before serving.