Brown the butter. Heat up a skillet on medium heat and add in the sliced butter. Allow it to melt, whisking occasionally to ensure that it melts evenly. The butter will begin to crackle and then foam. Stir frequently throughout these stages. Once it turns an amber-brown, you start to smell a nutty aroma, and you see little brown flecks in the pan, turn off the heat and immediately pour the butter into a separate heatproof bowl so that it doesn't burn. Let it rest until cool to the touch.
Once the browned butter is cool, transfer it to an electric mixer fitted with the paddle attachment, and add the cane sugar, brown sugar, egg, egg yolk, and vanilla. Beat on medium speed for around 1 minute, or until thick, creamy, and a little lighter in color.
Whisk the flour, salt, and baking soda (and pinch of nutmeg if using) in a separate bowl. Then add them to the wet ingredients and mix until just combined. Remove the bowl from the mixer and use a flexible spatula to fold in the chocolate chips.
Cover and chill the dough for 24 hours.
When ready to bake, preheat your oven to 350°F and line two cookie sheets with parchment paper. Let the dough warm up on the counter for 10-15 minutes to make it easier to scoop. Then, scoop 1.5 tbsp sized balls of dough and space them evenly on the cookie sheets. Give them plenty of room to breathe. I actually only placed 9 cookies on each sheet.
Bake for 12-14 minutes, or until edges are golden brown. Remove from the oven and let them rest for 10 minutes on the cookie sheets before transferring to wire racks to cool completely. Sprinkle with flaky sea salt and enjoy!