In a bowl, whisk together the flour, cocoa, baking soda, and salt.
3/4 cup flour, 1/2 cup unsweetened cocoa powder, 1/2 tsp baking soda, 1/2 tsp kosher salt
Using an electric mixer, beat the butter and sugar in a large bowl until light and fluffy, about 3 minutes. Beat in the egg yolk, vanilla and root beer concentrate. Reduce speed to low and gradually add the flour mixture, mixing just until incorporated. Fold in the sour cream.
Form dough into a rough thick square and wrap in plastic and chill in refrigerator until firm, (2-3 hours).
Preheat oven to 350 F. Roll out dough between 2 sheets of parchment to about 1/8" thick and slightly larger than a 14 x 10" rectangle. Transfer dough (still between parchment) to a large baking sheet and chill until firm (about 30 minutes). Remove top sheet of parchment and trim cookie to a large rectangle (14 x 10"). Bake cookie until dry and just set at edges (8-10 minutes). Transfer baking sheet to wire rack and let cool.
How to Assemble Ice Cream Sandwich
Let 2 pints of ice cream sit on counter until soft enough to mold (not completely melted however) Place a piece of parchment paper in a 9x9" square pan and spread the ice cream into the pan. Place in the freezer to refreeze into a square (you could also freeze into a rectangle by using a 9 x 12" pan, but the ice cream layer will be thinner).
Trim the edges of the cooled cookie so that you have a nice even rectangle, about 12" x 9". Cut this in half, forming two square cookies. Take the ice cream out of the freezer and run a knife dipped into hot water around the edges of the pan. Turn the pan over (ice cream side down) onto one of the cookie squares. Run a dishcloth under very hot water and place on top of the pan and then tap the pan gently with a knife so that the ice cream releases from the pan onto the cookie. Top with the other cookie and cut into the desired shapes of your sandwiches. Use a hot knife to cut out the shapes and move quickly. Wrap each individual sandwich in plastic wrap and place in freezer until firm.
Notes
**Please note that the nutrition facts are for the cookie part of the sandwich only. Nutrition and calories will vary on the ice cream part, depending on your selection of ice cream**Storage: ice cream sandwiches will keep in freezer for up to 2 weeks.