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

Combine Dry Ingredients. In a medium bowl, combine gluten-free flour, gluten-free oats, cinnamon, baking soda, and salt. Whisk to combine, then set aside.

Cream Butter & Brown Sugar. In the bowl of a stand mixer (or a large mixing bowl), combine softened butter and brown sugar. Beat on medium speed with a paddle attachment 2-3 minutes, or until smooth and fluffy.

Build The Dough. Scrape down the sides of the bowl, then mix in egg, molasses, and vanilla one at a time, mixing to incorporate each one well before adding the next. Add the dry ingredients, then mix on low speed until just combined and blended.

Scoop & Bake. Use a medium cookie scoop to measure 1 1/2 Tablespoon balls of cookie dough. Place 6 cookie dough balls on a prepared baking sheet and bake 9-10 minutes. Try not to over-bake, since you want the cookies to remain soft. If needed, gently shape cookies into perfect circles using a large round cookie cutter (or the back of a spoon).

Cool. Allow the cookies to cool 5-10 minutes on the cookie sheet before transferring cookies to a wire rack to finish cooling. Repeat until all the cookies are baked, alternating baking sheets with every batch so you don't put cool dough on a hot baking sheet. Let the cookies cool completely before frosting (so the frosting doesn't melt!)

Beat The Butter. When the cookies are cool, beat the butter in a stand mixer (or large bowl with a handheld electric mixer) 2-3 minutes, or until fluffy.

Combine. Add powdered sugar and mix on low speed, drizzling in 1 Tablespoon of milk and 1 teaspoon of the vanilla. (If needed, you can add more milk 1 teaspoon at a time.)

Whip. When the powdered sugar is absorbed, increase the speed to high and mix 1-2 minutes more, or until frosting is light and fluffy. Pause as needed, to scrape down the sides of the bowl. (If your frosting is too thick, you can add more milk 1 teaspoon at a time. If it's too thin, you can add powdered sugar 1 Tablespoon at a time.)

Frost The Cookies. Line cookies up in pairs (ideally they should be similar shape & size!). Flip over half of the cookies. (These will be the bottom half of the cookie sandwich.) Dollop or pipe about 1 1/2 Tablespoons of frosting onto each bottom half (don't spread it all the way to the edge, since the frosting will continue to spread when you add the top cookie). Top with the second cookie and gently press down to finish spreading the frosting.

Serve & Store. Enjoy right away or store in an airtight container at room temperature 1-2 days. Or, freeze up to 2 months.