In a large bowl or the bowl of a stand mixer, beat together the butter and sugar until light and fluffy. Add the eggs one at a time, followed by the vanilla, and mix well. Add the flour, baking powder, cinnamon, and salt, and mix until a firm dough forms. Chill 30 minutes.
Preheat the oven to 375ºF. Roll the dough into one inch balls and place on baking sheets lined with parchment. Flatten each ball slightly with your hand or with a drinking glass to be about 1/3-1/2 inch thick. Bake 8-10 minutes or until the bottom edges are just slightly golden brown. Remove and let cool before frosting.
To make the frosting, beat together the cream cheese and butter until light and fluffy. Add the powdered sugar and beat until smooth. Add the vanilla and milk as needed to reach desired consistency. Beat until light and fluffy. Pipe onto cooled cookies in a spiral shape and sprinkle with cinnamon.