Preheat oven to 350F. Line a 9x9x2-inch baking pan with foil. You’ll want the foil to hang over the sides a bit. Set aside pan.
In a medium bowl, combine butter and 1/4 cup shortening with a mixer on medium speed for 30 seconds. Next, add brown sugar, granulated sugar, and baking soda. Beat until combined. Scrape sides of bowl occasionally. Beat in egg and vanilla until combined. Beat in flour. Stir in miniature semisweet chocolate pieces and nuts if you’re using.
Spread dough evenly onto bottom of prepared baking pan. Bake for 25 to 30 minutes or until crust is evenly golden brown and center is set. Place on wire rack and cool in pan for 1 hour.
Reduce oven temperature to 325F. Using foil, lift baked mixture out of pan and transfer cookie to a cutting board; remove foil. Cut baked mixture into 9x1/2-inch slices then in half down middle (perpendicular to first direction). I like to use my pizza cutter for this. With cut sides down, place slices 1-inch apart on an ungreased cookie sheet. Bake in 325 degrees F oven about 20 minutes or until crisp, turning carefully halfway through baking time. Cool completely on the cookie sheet on a wire rack.
Melt chocolate and shortening over a double boiler until melted and smooth. Brush or spread one end of each cookie stick with melted chocolate mixture; let excess drip down sides of cookie. Place cookies on parchment paper or waxed paper; let stand about 1 hour or until set.
To Store: Place cookies in layers separated by waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months. Thaw cookies, if frozen, before serving