Preheat The Oven & Prep The Pans. To start, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and set aside.

Brown The Butter. In a light-colored saucepan, melt butter over medium heat, whisking constantly, until the butter is fully melted and begins to bubble. Continue cooking over medium heat and let it caramelize and brown. When the butter looks deeply golden under the foam, smells sweet and caramel-y, and you can see brown specks at the bottom, remove the pan from the heat. Transfer butter to a heatproof bool to cool to room temperature while you work on the next few steps.

Blot The Pumpkin. To remove some of the liquid from the pumpkin, layer 2 layers of paper towels on a plate. Spread the pumpkin puree out over the paper towels and top with another 1-2 layers of paper towels. Press down to soak up some of the liquid. (Ideally, the pumpkin puree should now be 1 cup or just under 1 cup. If you still have more than 1 cup of pumpkin, continue patting/blotting until you get down to about 1 cup.)

Combine The Dry Ingredients. In a medium bowl, combine gluten-free oats, gluten-free flour, cinnamon, nutmeg, ginger, cloves, baking soda, and salt. Whisk to combine.

Mix Butter & Sugar. In the bowl of a stand mixer (or a large mixing bowl), combine cooled brown butter, sugar, and brown sugar. Mix 1-2 minutes, or until the mixture looks like wet sand.

Finish The Wet Ingredients. Mix in the pumpkin puree, then add the egg yolk and mix to combine. Mix in the vanilla and scrape down the sides of the bowl.

Mix In The Dry Ingredients. Next, add the dry ingredients and mix until just combined. Scrape down the sides of the bowl again and check that everything is blended evenly.

Scoop & Bake Cookies. Use a medium cookie scoop to measure 2 Tablespoon balls of dough. (I do NOT roll these smooth, I just scoop them directly onto a prepared baking sheet to avoid packing the dough together.) Bake 6-8 cookies at a time for 12-14 minutes. Let the cookies cool 2 minutes on the baking sheet before transferring to a wire rack. Repeat this process, alternating baking sheets with each batch so you don't put cool dough on a hot baking sheet.

Mix Up The Glaze. When all the cookies are baked, start the glaze. In a medium mixing bowl, combine powdered sugar, 2 Tablespoons milk and the vanilla. Mix in the additional milk 1/2 teaspoon at a time, as needed, until you have a smooth, thick vanilla glaze that can slowly drip down from your whisk. Keep in mind that you want it quite thick so it looks mostly opaque on the cookies.

Glaze Cookies. Working one cookie at a time, hold the cooking in your hand face-down and lower into the glaze until the cookie JUST touches the surface of the glaze. Gently shake off any extra glaze, then set the cookie glaze side up on a wire rack to set. Ideally, you want the glaze to cover the ridge of the top of the cookie, with little cracks visible in between. Repeat until all cookies are glazed.

Serve & Store. Let the glaze set completely, then enjoy cookies. Store leftover pumpkin oatmeal cookies in an airtight container at room temperature 2-3 days, or in the freezer up to 2 months. (When storing, store in a single layer to avoid messing up the glaze!)