In a large bowl, beat the butter until creamy and fluffy (about 2 minutes). Add the peanut butter and sugars and beat for another 2-3 minutes. Add the pudding mix and beat for another minute.
Add the eggs and vanilla and beat for another 2 minutes.
In a separate bowl, stir together the flour, baking soda and salt. Add this mixture to the butter mixture and mix just until combined.
Carefully fold in the crushed Oreo crumbs.
Use a cookie scoop to scoop the dough onto a prepared cookie sheet, placing the cookie dough balls about 2 inches apart.
Bake cookies for about 10 minutes – do not overbake! Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.