In a large bowl, cream butter and sugars until light and fluffy. Beat in milk and vanilla. Combine the flour, baking soda and salt; gradually add to creamed mixture and mix well. Stir in chocolate chips. Cover and refrigerate for 1 hour or until easy to handle.
On a lightly floured surface, roll out dough to 1/4-in. thickness. Cut with a 2-in. round cookie cutter; place 1 in. apart on ungreased baking sheets. Bake at 375° for 8-10 minutes or until lightly browned. Cool for 2 minutes before removing to wire racks.
Spread about 1 tablespoon of ice cream on half of the cookies; top with remaining cookies. Wrap each sandwich in waxed paper; freeze for several hours or overnight.