Preheat the oven to 350 degrees. Line a baking sheet with a silpat mat.
Combine the flour, butterscotch pudding mix, and baking soda in a small bowl.
Beat the butter in a large bowl with a hand mixer until creamy.
Add the brown sugar and eggs.
Gradually add the flour mixture to the wet mixture until just combined.
Add most of the butterscotch chips and white chocolate chips then mix.
Drop dough by rounded spoonfuls 2 inches apart onto the prepared baking sheet. Add a few of the remaining butterscotch chips and white chocolate chips to the top of each cookie.
Place into the oven and bake for 8-10 minutes, or until set. Cool on the baking sheet for 2 to 3 minutes; remove to wire racks to cool completely.