In a mixing bowl, cream together the butter and sugar until light and fluffy. Add the egg and vanilla extract and mix well.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients and mix until a soft dough forms.

Flatten the dough into a disk, wrap in plastic wrap, and chill for 1 hour.

On a lightly floured surface, roll the dough into a rectangle about 1/4-inch thick.

Brush the melted butter over the surface, then sprinkle evenly with brown sugar and cinnamon.

Gently roll the dough up from the long side into a log. Wrap and chill for another 15–20 minutes to firm up.

Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.

Slice the log into 1/2-inch thick rounds and place them on the prepared baking sheet.

Bake for 10–12 minutes, or until edges are lightly golden. Cool completely on a wire rack.

Mix the glaze ingredients in a small bowl until smooth, then drizzle over the cooled cookies.