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Preheat oven to 350 degrees. Line baking sheets with parchment paper and set aside.
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In a stand mixer or large mixing bowl with hand mixer, cream together butter, eggs, sugar, brown sugar, and vanilla until smooth.
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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.
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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.
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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.
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Store cookies in airtight container for 3 days at room temperature or for up to 3 months in the freezer.