Heat oven to 350 degrees F. Whisk together flour, baking soda and salt in a medium bowl. With an electric mixer, beat together butter and brown sugar on medium-high speed for 1 minute. Add egg and beat until smooth. On low, beat in vanilla and flour mixture just until blended. Stir in mini chips.
2. Drop batter by the teaspoonful onto two large baking sheets (you should have 5 dozen cookies). Bake at 350 degrees F for 14 minutes or until slightly browned. Cool 1 minute on pans, then transfer directly to a rack to cool completely.
On medium speed, beat together confectioners' sugar, butter and milk until smooth, thick frosting is created. Spread about 2 teaspoons of filling onto flat side of one cookie. Press a lollipop stick into frosting, then sandwich with a second cookie (flat side down). Refrigerate until firm.