Grease a cookie sheet. Beat the butter and the 1/4 cup shortening. Add brown sugar, milk, vanilla, and salt. Beat in flour. Stir in chocolate pieces. Cover and chill for 30 minutes. While waiting, filling can be made. Combine white pieces (3/4 cup) and milk in a small saucepan, then cook over low heat until melted. Let cool. Stir in mint extract and food coloring. When dough is finished chilling, divide in half and refrigerate the second half while working with the first. Roll one half into a 12 x 6 rectangle on a floured surface. Spread half of the filling up to about 1/2 inch from the edge. Fold the rectangle in half and seal all the edges. Repeat the process for the other half of the dough and filling. Bake these at 350º F for about 15-20 minutes. Cut them crosswise into 3/4-inch strips. While cooling, make frosting with 1/2 cup white pieces and shortening. Pipe onto the tops in an attractive squiggle or any design.
NOTE: When folding the cookie outside over the filling, try to make sure there are as FEW cracks as possible and that it is as sealed as it can be. The mint filling has a tendency to try to bubble up and escape. Also, these are plenty sweet, so icing is optional.