Preheat oven to 350 degrees Fahrenheit and line cookie sheets with nonstick baking mats or lightly spray them with nonstick cooking spray.

In the bowl of an electric mixer, cream together butter, shortening, brown and granulated sugars, vanilla, and eggs. Add flour, baking soda, salt and pudding mix and mix until incorporated. Stir in chopped vanilla wafers and white chocolate chips. Form dough into 1 1/2 to 2" balls and place at least 2" apart on the cookie sheet. Press the dough balls down with the palms of your hand to flatten. Press additional white chocolate chips or vanilla wafers in the top, if desired.

Bake for approximately 8 to 9 minutes. Allow cookies to cool for a few minutes on the cookie sheet before carefully removing them to a cooling rack to cool completely. Store in an airtight container.