Prepare the Cookie Dough: In a small bowl, whisk together ground flax and hot water. Set aside. In medium bowl, whisk together white rice flour, sorghum flour,baking soda, and salt.
In bowl of stand mixer fitted with paddle attachment (or large bowl), cream together shortening and sugars on medium high speed. Cream until a thick paste forms, about 30 seconds. Add flax mixture and vanilla. Cream until mixture is light and fluffy, about 45 seconds.
Stop mixer and scrape down bottom and sides of bowl. Add dry ingredients. Turn mixer on to medium speed. Mix until dough forms, about 30 seconds. Turn off mixer and add chocolate chips. Turn mixer on to low speed. Mix until chips are combined, about 15 seconds.
Drop dough, about 1/2 teaspoons each, onto prepared baking sheet. Cover pan with plastic wrap and chill until dough balls are firm, about one hour.
Prepare the Ice Cream: Remove ice cream from the freezer. Place it on the counter to soften, about ten minutes. Using a large spoon, scoop softened ice cream, working from the outside of the carton toward the center, into a freezer-safe container. As you work, dot the ice cream with chilled dough balls. (If the ice cream begins to soften too much, return containers to the freezer, allow ice cream to harden, and then finish the recipe.)
After all ice cream has been transferred, smooth ice cream with the back of a spoon.
Press a piece of plastic wrap directly onto the surface of the ice cream. Cover container with a tight fitting lid. Freeze until firm and serve.