Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, combine the gluten-free rolled oats, gluten-free flour, baking soda, salt, and ground cinnamon. Set aside.
In a large mixing bowl, cream together the softened unsalted butter, brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes.
Add the vanilla extract and eggs to the butter mixture, mixing until well combined.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined.
Fold in the gluten-free rolled oats and butterscotch chips until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes until edges are lightly golden.
Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.