In a deep-sided saucepan, brown the butter until golden, nutty, and there are plenty of dark bits on the bottom. Remove the pan from the heat, scrape up the brown bits and cool until your hand can touch the bottom of the pan.
In the bowl of a stand mixer, or using an electric mixer, blend sugars with the eggs until thick, fluffy, and almost doubled in volume, about 5 minutes. Add vanilla and nutmeg, and salt. Thoroughly mix in butter, including all the brown bits. In a medium bowl, whisk together flour, almond and oat flour, and baking soda until combined. Add to egg butter mixture and blend just until the mixture is combined. It will look more like a batter than dough. Add the chocolate chips and fold in with a spatula. Cover the bowl and refrigerate for 45 minutes to one hour. Scoop dough into ¼ cup-sized balls onto a parchment-lined pan. There should be 24 dough balls. Cover with plastic wrap and refrigerate for another hour or two and even overnight.
Preheat oven to 350°F. Line two baking sheets with parchment paper. Place 6 dough balls on each pan. Bake, 14-16 minutes or until the cookies are dark golden brown on the edges and golden in the center. Cool in the pan for five minutes, then transfer cookies to a rack to cool completely. Terrific, just warm.