Beat shortening and butter together in a bowl using an electric mixer until smooth and creamy. Add brown sugar and white sugar and beat until smooth. Add eggs, vanilla extract, and baking soda; beat until well mixed.
Slowly mix enough flour into butter mixture until a thick dough forms; fold in chocolate chips. Spoon small mounds of dough onto a baking sheet, about 1-inch apart.
Bake in the preheated oven until edges are lightly browned, 8 to 9 minutes.