In a large bowl using an electric mixer, combine the ½ cup unsalted butter and ½ cup sugarand mix until light and fluffy, about two minutes.
Add the 1 large egg and 1 teaspoon pure vanilla extract and mix until well combined.
Beat in the 2 ¾ cups gluten-free oat flour or all-purpose flour, ½ teaspoon baking powder, and ¼ teaspoon fine sea salt. Mix well to combine, until the dough looks thick and uniform. Cover the bowl with a piece of plastic wrap and place it 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 oat 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.
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.
Cookies will keep in an air-tight container at room temperature for 5 days.
Notes
About the amount of sugar ... I realize that cutting the sugar to ½ cup may not be for everyone. My gluten free sugar cookies recipe calls for 1 cup of sugar, and it's plenty sweet. If ½ cup is just too little sugar, try ¾ cup of sugar instead.
If you want a more naturally sweetened option, try maple sugar for the granulated sugar. This gives a lovely hint of maple flavor as well as sweetness. I've also made these cookies with honey, which I find to be sweeter than granulated sugar. It also gives the cookies a light floral taste.
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 until a smooth dough forms (it will!)
Dairy-free: I like swapping softened coconut oil for the butter for a dairy-free version, and dairy-free butter also works great.
Make them vegan: Substitute a non-dairy option for the butter, and either omit the egg or use a flax egg substitute.
Make ahead: The dough may be stored, wrapped in plastic or in an airtight container, for up to 3 days in the fridge. Let it warm up a bit at room temperature before rolling out and cutting.