In a medium bowl, cream the shortening, white sugar, and brown sugar together with a wooden spoon. Add eggs and vanilla, mix well. Sift together the flour, baking soda and salt, stir into the creamed mixture. Finally stir in the semi sweet chips and the white chips, if the batter is too stiff, you may need to use your hands.
Drop cookies by heaping spoonfuls onto unprepared cookie sheets. Bake for 7 to 10 minutes in the preheated oven. I always like to take my cookies out of the oven when they are light brown and not yet set. It creates a softer cookie. Allow cookies to cool for a few minutes on the baking sheet before removing to cool on wire racks.