Preheat oven to 350°F. Line baking sheets with parchment paper.
Cream butter and sugar in a stand mixer until smooth. Add eggs and vanilla extract. Mix well.
Add flour, baking powder, and cinnamon. Mix until combined.
In a small bowl, mix sugar and cinnamon for coating. Reserve 1 tablespoon.
Scoop dough into balls, roll in coating, and place on baking sheets. Flatten to ½–¾ inch.
Bake 10–12 minutes until set. Cool completely.
For frosting: Beat butter, cinnamon, half of the powdered sugar, and milk. Add remaining sugar and whip until fluffy.
Pipe frosting onto cooled cookies. Sprinkle with reserved cinnamon sugar.
