Preheat oven to 350 degrees. Line baking sheets with parchment paper and set aside.
In a stand mixer or large mixing bowl with hand mixer, cream together butter, eggs, sugar, brown sugar, and vanilla until smooth.
Add salt, baking soda, and gluten free flour and mix until well incorporated. Add butterscotch morsels and milk chocolate chips and mix on low speed or with a wooden spoon.
Drop walnut sized balls of cookie dough 2" apart on cookie sheet and bake at 350 degrees for 10-12 minutes or until lightly brown on edges and tops of cookies.
Slide parchment paper with cookies onto cooling rack and allow cookies to cool completely. Continue baking cookies, one pan at a time, until dough is gone.
Store cookies in airtight container for 3 days at room temperature or for up to 3 months in the freezer.