In a large mixing bowl, cream together the butter and sugar until the mixture is light and fluffy.
Scrape down the sides, then add in the eggs and vanilla extract. Beat until well combined.
Scrape down the sides again and add in the flour, baking powder, and cinnamon. Mix until everything is well combined.
Scoop out 1/3 cup portions of dough and roll each into a ball. Repeat with the remaining dough.
In a separate bowl, mix the sugar and cinnamon. Set aside a few tablespoons of this mixture for sprinkling on the cookies after frosting.
Roll each dough ball in the cinnamon-sugar mixture, then flatten them gently into a hockey puck shape.
Place six cookies per baking sheet. Bake at 350°F for 14-17 minutes, until the centers are puffed and no longer glossy.
While the cookies cool, prepare the frosting. Whip the butter until smooth, then gradually add the powdered sugar, one cup at a time, thinning with a bit of milk after each addition to achieve a thick frosting consistency.
Once all the powdered sugar is incorporated, mix in the ground cinnamon thoroughly.
Transfer the frosting to a piping bag with a large round tip or a gallon-sized zip-top bag with a corner cut off. Pipe the frosting onto the warm cookies in a spiral, starting from the center and working your way outwards.
Sprinkle the reserved cinnamon-sugar mixture on top. Serve warm and enjoy!