First, Brown The Butter. In a light colored saucepan, melt butter over medium heat, whisking or stirring nearly constantly until the butter is fully melted and begins to bubble. Continue cooking the butter over medium heat (you’ll hear it popping and bubbling) to let it caramelize and brown. After 6-8 minutes or so, the butter will begin to foam and bubble. When the butter looks deeply golden, smells caramel-y and sweet and you can see that the butter solids are starting to brown, turn off the heat. Remove the pan from the heat and transfer to a heatproof bowl–either the bowl of your stand mixer or a large mixing bowl–to cool for about 15-20 minutes. (Small brown specks are ok! That’s what you’re going for.)

Pulse The Oats. Add the rolled oats to a food processor or blender. Pulse 10-12 times or so, until you can see some powdery bits, some broken oats, and some whole oats. (You do NOT want to grind the oats into a fine flour, and you don’t want them all whole.) Set the oats aside.

Combine Butter & Sugars. Add brown sugar and sugar to the slightly cooled brown butter and stir to combine. The mixture will look like wet sand at this point.

Mix In Eggs & Vanilla One At A Time. Add one egg to the dough and stir until fully incorporated. Then, add the next egg and stir till fully incorporated. Add vanilla, and mix until combined.

Add Dry Ingredients. Next, add the oats you pulsed to the bowl, along with gluten-free flour, cinnamon, nutmeg, salt, and baking soda. Stir until just combined.

Chill For 30 Minutes. Cover the dough and chill in the fridge 30 minutes or so while you preheat the oven.

Preheat The Oven & Prep The Pan. Then, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and set aside. (This way you can alternate baking sheets with each batch so you don’t put cold dough on a hot baking sheet!)

Scoop & Roll The Dough. Use a medium cookie scoop (2 Tablespoons) to scoop even balls of dough. Roll the dough balls between your palms to smooth them out a bit, then place 6-8 cookie dough balls on a baking sheet. Return the rest of the dough to the refrigerator in between batches.

Bake & Cool. Bake just one cookie sheet at a time for 8-10 minutes, or until the cookies are set around the edges and look just done in the center. (Try not to over-bake, and keep in mind that the cookies will continue to cook after you pull them out of the oven.) Let the cookies sit on the baking sheet 1-2 minutes before transferring to a wire rack to finish cooling completely. Repeat this process, alternating between baking sheets with each batch, until all the cookies are baked.

Mix Up The Glaze. When the cookies have cooled completely, mix up the vanilla glaze. In a small bowl, combine powdered sugar, milk or cream, and vanilla extract or vanilla bean paste. Whisk or stir with a fork until the glaze is smooth and very thick, with no lumps. If needed, you can add additional milk 1/2 teaspoon at a time, until the glaze is thin enough to dip the cookies into, but keep in mind, you want it quite thick so it’s mostly opaque on the cookies.

Dip The Cookies. Working one cookie at a time, hold the cookie in your hand face-down and lower into the glaze just until the cookie touches the surface of the glaze. Shake off excess glaze, then set the cookie glaze side up on a wire rack to set. Ideally, you want the glaze to cover the ridges of the top of the cookie, with little cracks visible in between. Repeat until all cookies are glazed.

Set, Serve & Store. Let the glaze set completely then enjoy the cookies. Store leftover cookies in an airtight container at room temperature 3-4 days or in the freezer up to 2 months.