In the bowl of stand mixer fitted with a paddle attachment, cream the butter and sugars on medium speed for 1-2 minutes or until light and fluffy. Scrape down the sides of the bowl. Add the eggs and vanilla and mix for another 1-2 minutes.
Mix in the flour, cinnamon, baking powder, and salt. Mix until just combined. Cover and refrigerate the dough for at least 1 hour.
In a microwave safe bowl warm the butter, brown sugar, and cinnamon until melted and fully combined.
Divide the dough into 2. On a lightly floured surface, roll out each half to a 12x6 inch rectangle. Spread 1/2 of the cinnamon mixture over each rectangle. Gently roll each rectangle into a log, to create a 12 inch log (roll lengthwise). Place each log on a large plate or small baking sheet and chill for 10 minutes, but no longer!
Preheat the oven to 375°F. Line a baking sheet with parchment paper.
Remove the logs from the fridge and cut into 1” inch segments.
Place the cookies on the baking sheet leaving 2 inches between each cookie.
Bake for 9-12 minutes. Remove the cookies from the tray while they are still warm. Transfer to a wire rack to cool to room temperature.
Drizzle the icing overtop of the cookies.
Icing: whisk the powdered sugar, milk, and vanilla until smooth.
The dough shouldn't be cold when you bake the cookies, hence only chilling the dough for 10 minutes. The short chill time just helps with slightly setting the butter and making the dough easier to cut.