01 - Combine flour, baking powder, baking soda, and salt in a medium bowl. Whisk until evenly blended.
02 - In a large bowl, use an electric mixer or whisk to beat the softened butter, creamy peanut butter, granulated sugar, and light brown sugar until pale and fluffy, about 2 to 3 minutes.
03 - Beat in the egg and vanilla extract until fully incorporated.
04 - Gradually mix the dry ingredients into the wet mixture until a cohesive dough forms.
05 - Transfer dough onto parchment paper. Place another sheet of parchment on top and use a rolling pin to flatten to a 1/4-inch thick rectangle, approximately 10x14 inches.
06 - Brush melted butter evenly over the dough surface. Sprinkle with light brown sugar and ground cinnamon.
07 - Carefully roll up the dough lengthwise into a tight log. Wrap in parchment paper and refrigerate for at least 1 hour until firm.
08 - Set oven to 350°F. Line a baking sheet with parchment paper.
09 - Using a sharp knife, cut the chilled dough log into 1/2-inch thick rounds. Arrange cookies about 2 inches apart on the prepared sheet.
10 - Bake for 10 to 12 minutes, until edges are lightly golden. Let cookies cool on the pan for 5 minutes, then transfer to a wire rack.
11 - Stir powdered sugar with milk until smooth. Drizzle the icing over cooled cookies.