Preheat oven. Adjust oven rack to middle position and heat oven to 350 degrees Line two baking sheets with parchment paper.
Make the dough. Stir together melted butter and brown sugar until smooth. Add egg and vanilla extract. Mix until smooth. The mixture will look like caramel sauce. Add the gluten-free flour, cinnamon, baking soda, and salt. Sir until you don’t see any streaks of flour. Add the oats and chocolate chips or raisins. Mix until combined.
Scoop and Bake. Drop dough, about two tablespoons each, onto one of the prepared baking sheets. Space dough about one inch apart. These don’t spread much. Bake until set, about 12 minutes.
Cool. Remove the pan from the oven and allow the cookies to cool on the pan for minutes. (While they cook, bake the remaining dough on the second baking sheet.) Transfer cookies to a wire rack and allow to cool completely.
Store. Keep the cookies covered on the counter for up to four days or freeze for up to three months. To freeze cookies: place in a freezer container and separate layers with a piece of wax or parchment paper. Thaw overnight on the counter.