Preheat oven to 375 degrees.
In a small bowl, sift together flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer, cream butter and sugar until well combined. Add egg, milk, and vanilla to the sugar mixture and beat until well blended. Gradually add flour and mix until completely combined.
Using a medium-sized ice cream scoop, scoop a ball of dough onto a piece of parchment paper placed on an ungreased cookie sheet. Place in the preheated oven for 8 minutes, or until the cookies are golden. Allow cookies to cool for about 2 minutes and remove to a cookie rack. When completely cooled, ice cookies or store them in an air-tight container for 7 to 10 days.