Sift together flour, salt, cream of tartar, baking soda. Add the 1.7 oz of instant pudding to this mixture and mix well. Set aside.
In a separate bowl, beat butter and shortening until creamed and light in color. Slowly add the sugars. Add vanilla extract and continue to mix. Slowly add the milk 1 tbsp at a time and mixing well between additions. Add the eggs one at a time and beat between each addition.
Mix together dry and wet mixtures and knead with your hands. Form into a ball, wrap in plastic wrap and refrigerate for 2 to 3 hours. When ready to bake a batch, form into 1-inch balls and place on an ungreased cookie sheet an inch apart from each other. Bake in a preheated oven at 350 degrees for 8 to 10 minutes. Let cookies completely cool before eating. The cookies taste great covered with buttercream frosting.