In a large bowl using an electric mixer, combine the butter and sugar and mix until light and fluffy, about two minutes.
Add the egg and vanilla extract and mix until well combined.
Beat in the gluten-free flour, baking powder, and salt. Mix well, until the dough looks thick and uniform. Cover the bowl with a piece of plastic wrap and place in in the fridge to chill for at least 10 to 15 minutes.
When ready to roll out cookies, preheat the oven to 350°F. Take the cookie dough out of the fridge and let the dough rest a few minutes at room temperature to soften. Then line a work surface with a large piece of parchment paper. Place the cookie dough in the center and sprinkle with gluten-free flour. Flour a rolling pin and roll out the dough into a ¼-inch thick sheet. Use cookie cutters to cut the dough into shapes and place them on the cookie sheet. Decorate with sprinkles if you wish!
Place in the oven and bake for about 8-10 minutes depending on how crisp you wish the cookies to be. I found 9 minutes to be perfect.
Remove cookies from oven and cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Notes
Rest the dough: Let the dough rest and chill in the fridge for at least 15 minutes before baking, or up to 3 days in advance of baking. Oat flour, like all gluten-free flours, benefits from a rest to let it absorb liquids. This
Use room temperature ingredients: Bring ingredients to room temperature before using. This is particularly important for the butter - if it's nice and soft, it will incorporate better into the batter, making for a smoother and more uniform cookie.
Don't worry if the dough is crumbly. When you're combining the dough, it may seem a bit dry and crumbly. Don't worry! Keep beating the ingredients until they come together. If needed, you can use your hands to squeeze and knead the dough together a few times.
Make them dairy-free: You can easily make these oat flour cookies dairy-free. Swap a non-dairy butter or slightly softened coconut oil for the butter.
Make them refined sugar-free: I love to use maple sugar when I make sugar cookies. The subtle, natural sweetness of the maple sugar take them over the top (and, make them refined sugar-free!).
Use a single-origin flour. You can easily make these into sorghum, brown rice, or oat flour sugar cookies by substituting 300 grams of a single gluten free flour of your choice.