01 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt; set aside.
02 - In a large bowl, use an electric mixer or whisk to beat butter, peanut butter, granulated sugar, and brown sugar until light and fluffy, about 2 to 3 minutes.
03 - Add egg and vanilla extract; mix until fully incorporated.
04 - Gradually blend the dry mixture into the wet ingredients, mixing until a smooth dough forms.
05 - Place dough between two sheets of parchment paper and roll into a 10 by 14-inch rectangle, approximately 1/4 inch thick.
06 - Brush melted butter evenly over the surface. Sprinkle brown sugar and cinnamon evenly on top.
07 - Starting from the longer edge, roll dough tightly into a log. Wrap in parchment and refrigerate for at least 1 hour until firm.
08 - Preheat oven to 350°F. Line baking sheet with parchment paper.
09 - Cut the chilled log into 1/2-inch thick slices. Arrange cookies 2 inches apart on prepared baking sheet.
10 - Bake for 10 to 12 minutes, until edges are lightly golden. Leave cookies on the sheet for 5 minutes, then transfer to wire rack to cool completely.
11 - For optional icing: combine powdered sugar with milk in a small bowl until smooth. Drizzle over cooled cookies.