Preheat the oven to 350 F.
In a large bowl, sift together arrowroot flour, all-purpose flour, baking powder, and salt. Set aside.
In another mixing bowl, cream butter and sugar with an electric mixer until creamy and fluffy.
Beat in eggs one at a time, just until incorporated. Beat in vanilla extract.
Gradually add the dry ingredients to the mixing bowl, starting at low speed to moisten and then increasing the speed to incorporate fully.
Beat just until the batter is smooth. DO not overbeat.
Transfer the batter into a cookie press. Dispense the batter in a single press onto an ungreased baking sheet, leaving about 1 and ½ inch space in between.
Bake in the preheated 350 F oven for 12 to 15 minutes, or until the undersides are starting to turn golden.
Allow to cool completely in the pan. To remove, simply slide a cookie with your fingers until it releases. Do not use a spatula to lift the cookies as they're fragile and might break.