Preheat the oven to 350 degrees Fahrenheit. Line a cookie sheet with parchment paper or a silicone liner. Set aside.
In a large bowl, cream together the sugars and butter, until well mixed, and light and creamy, about 2 minutes.
Add in eggs, vanilla, and mix until just combined.
Add in the flour, pudding mix, salt and baking soda. Stir in completely until you have a nice soft dough.
Fold the graham cracker pieces and white chocolate chips evenly into the dough.
Scoop the cookie dough into 2 Tablespoon sized scoops, and roll them into smooth balls.
Place about 8 cookie balls, on to each prepared baking sheet. Place them about 2 inches apart.
Bake the cookies for 8-9 minutes until lightly golden on the sides, and the tops are just barely set. They might not look all the way done.
Allow cookies to cool on cookie sheet for about 8 minutes on the cookie sheet, as they'll keep cooking as they are there. Then transfer them to a cooling rack to cool completely.