Brown the butter. Melt the butter in a light-colored skillet or saucepan over medium-low heat. Stir constantly with a rubber spatula as the butter foams. Keep stirring until the butter turns a deep amber color and releases a nutty aroma, then take the pan off the heat. Immediately transfer the butter to the bowl of a stand mixer or a large mixing bowl. Make sure to scrape all the golden browned bits from the bottom of the pan. Allow the brown butter to cool in the bowl for 15-20 minutes.
Add the sugar. Once the butter has cooled, add the regular cane sugar and dark brown sugar to the bowl. Mix with a whisk attachment on medium speed for 1 minute.
Mix in the eggs and vanilla. Add the large egg, egg yolk, and vanilla extract. Continue to mix until combined and smooth.
Add the dry ingredients. Whisk together the flour, almond flour, baking soda, and salt in a medium-sized bowl. Add the dry ingredients to the wet ingredients and mix at medium speed until combined. Use a rubber spatula to fold in any remaining flour bits at the bottom of the bowl.
Chill the dough. Cover the dough and refrigerate for 2 hours or overnight. If the dough has chilled longer than 2 hours it may be a bit difficult to scoop, therefore I recommend allowing the dough to come to room temperature for 20-30 minutes before baking.
Scoop and roll. When you are ready to bake the cookies preheat the oven to 350°F. Line two large baking sheets with parchment paper. Use a medium cookie scoop (1.5 Tablespoon size) to scoop the cookie dough into 35-gram balls (weigh on a food scale). Then roll each ball of dough in between your palms until smooth.
Bake. Place 5-6 balls onto a prepared baking sheet, about 2- inches apart, and bake for 9-10 minutes, or until the edges are golden brown and the center looks pale and slightly underdone. Remove the tray from the oven and sprinkle the top of each cookie with flaky sea salt.
Round out the cookies. To create perfect circular cookies, round them out with a circular cookie cutter. Place it over the top of each cookie, and gently swirl in a circular motion until a perfect circle forms. Let the cookies rest for 2-3 minutes on the baking sheet, before transferring to a wire rack to finish cooling.