Preheat oven to 375 degrees F.
Beat the shortening, sugars and vanilla in large bowl with mixer on medium speed until well blended. Beat in eggs, then beat in mayonnaise.
Mix together the cake flour, salt and baking soda, then add it to the batter and stir to make a soft dough.
Stir in the chocolate chips.
Using 2 tablespoons of dough for each cookie, shape into mounds on parchment lined baking sheets OR put them on plastic wrap lined dinner plates and chill until ready to bake.
Bake at 375 for 10-12 minutes. Alternatively, bake at 350 for slightly longer.
Let cool for 2 minutes, then transfer to a wire rack to cool completely.