Brown & Cool Butter. Before you start the cookie dough, brown the butter. Dice the butter into cubes then add to a medium saucepan. Cook over medium heat 8-10 minutes, stirring constantly until the butter is golden brown and fragrant. Remove from the heat and pour into a bowl to cool. (Get step-by-step instructions for browning butter here!)
Combine Dry Ingredients. In a medium bowl, combine gluten-free flour, cornstarch, cream of tartar, cinnamon, baking soda, and salt. Whisk until well combined, then set aside.
Mix Wet Ingredients. In the bowl of a stand mixer (or a large mixing bowl), combine COOLED brown butter, brown sugar, and granulated sugar. Mix to combine. Drizzle in pure maple syrup, then add egg, egg yolk, vanilla extract, and maple extract. Mix until evenly combined.
Add Dry Ingredients. Scrape down the sides of the bowl, then add the flour mixture. Mix until just combined, with no floury patches left.
Chill Dough 30 Minutes. Cover the dough and chill in the fridge just 30 minutes while you preheat the oven and prep your pans. (I don't recommend chilling longer than 30 minutes, or the dough can be hard to work with.)
Preheat & Prep. While the dough chills, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and set aside. In a small bowl, combine granulated sugar and cinnamon to make cinnamon sugar mixture.
Scoop & Roll Dough. Use a medium cookie scoop to measure 2-Tablespoon balls of cookie dough and roll smooth between your hands. Roll each cookie dough ball in cinnamon sugar then place 6-8 cookies on a baking sheet. (Return the rest of the dough to the fridge in between batches.)
Bake & Cool. Then, bake the cookies 9-12 minutes in preheated oven until the edges are set and the centers look slightly underdone. (The remaining heat will finish cooking them through.) Let the cookies cool 1-2 minutes on the cookie sheet before transferring to a wire rack to cool completely. Repeat process, alternating cookie sheets with each batch so you don't put cold cookie dough on a hot baking sheet.
Serve & Store. Enjoy cooled cookies right away or store in an airtight container at room temperature 2-3 days. If desired, you can freeze cookies up to 2 months.