Preheat your oven to 350°F (175°C). Gather and measure all ingredients.
In a medium bowl, combine rolled oats, gluten-free flour, baking powder, baking soda, salt, and ground cinnamon. Stir until well mixed.
In a separate large bowl, cream together softened butter, brown sugar, and granulated sugar until light and fluffy. Add egg and vanilla extract, mixing until well combined.
Gradually add dry ingredients to wet mixture, mixing until just combined.
Scoop tablespoon-sized portions of dough, roll into balls, and place on a baking sheet spaced 2 inches apart.
Bake for 10-12 minutes until edges are lightly golden. Cool on baking sheet for 5 minutes before transferring to a wire rack.
Prepare icing by whisking together powdered sugar, milk, and vanilla extract until smooth.
Once cookies are cool, drizzle icing over the top using a spoon or piping bag. Allow icing to set before serving.