Whisk the dry ingredients. In a medium bowl, whisk together the gluten-free flour, almond flour, baking soda, and salt. Set aside.
Brown the butter. Melt the butter in a light-colored skillet or saucepan over medium-low heat. Using a rubber spatula, stir continuously as the butter begins to foam. Once the butter under the foam changes to a toasty brown-golden color, and smells sweet with a nutty aroma, remove the pan from the heat. Quickly pour the butter into the bowl of your stand mixer or a large mixing bowl. Make sure to scrape out all of the toasty brown bits from the bottom of the pan and into the bowl. Let the brown butter cool in the bowl for 10 minutes, or until it’s no longer hot to the touch.
Chop the macadamia nuts. While the butter is cooling, chop the roasted macadamia nuts into small chunks and set aside.
Combine the wet ingredients. When the butter has cooled, add the sugar and dark brown sugar. Mix with the whisk attachment on medium speed for 1 minute. Add the large egg, egg yolk, vanilla extract, and almond extract. Whisk until just combined, do not over-mix. Turn off the mixer.
Add the dry ingredients. Using a rubber spatula, fold the dry ingredients into the wet ingredients until just combined. Be careful to not overwork the cookie dough.
Add the white chocolate chips and nuts. Fold in the white chocolate chips and chopped macadamia nuts. Cover the bowl and refrigerate for at least 2 hours.
Preheat the oven to 350°F.Scoop and roll cookie dough balls. (If chilling for longer than 2 hours, allow to sit at room temperature for at least 20-30 minutes before rolling and baking). Line two large baking sheets with parchment paper. Scoop and roll the cookie dough into 40-gram balls. Roll each ball of dough in between your palms until smooth, and then place 6 balls onto a prepared baking sheet. Bake and cool. Bake for 9-10 minutes, or until the edges are a golden brown color and the centers look just underdone. Top with flaky sea salt, and let them cool for 5 minutes on the baking sheets before transferring them to a wire cooling rack to finish cooling. (To achieve perfectly round cookies, place a large cookie cutter or glass cup over the top of each cookie and gently swirl in a circular motion until they form a perfect circle.)