In a large mixing bowl or the bowl of a stand mixer, combine cooled brown butter, white sugar, brown sugar, vanilla, salt, nutmeg, baking powder, and baking soda.
Start on a low speed to moisten, then increase speed to medium until batter is well combined, about 5 minutes. You may need to pause the mixer and scrape down the sides of your bowl halfway through the process to ensure your ingredients are incorporated.
Scoop golf-ball sized portions of your cookie dough onto ungreased aluminum baking sheets, with about 2 inches between each of them. Bake for 13-14 minutes.