Brown the butter: set a pan over medium low heat and add the butter. Cook as the butter melts, then starts to sputter. Eventually it will go quiet and foam, you’ll see little cream colored bits that look like panko in the bottom of the pan. Use a rubber spatula to stir the butter, scraping the edges of the pan to make sure those bits cook evenly. They will start turning brown and when they are all a rich brown color, transfer to a medium sized heatproof bowl. Scrape up all the bits into the bowl. Let cool for about 5-10 minutes.
Add the milk, brown sugar and fine granulated sugar, salt and vanilla and whisk very well. Set the mix in the microwave for 30 seconds then whisk it vigorously.
Add the egg and immediately whisk; don’t wait or the heat of the sugar/butter will ‘cook’ the egg. Whisk vigorously until the mix is well combined.
Add in the flour and baking soda and stir until the dough is smooth. Cover the dough with a clean kitchen towel and leave at room temperature for an hour. After the hour, add the nuts and chopped chocolate and set in the fridge for 3-4 hours, or overnight.
Take the dough out of the fridge about two hours before baking to bring it to room temperature. Prep two cookie sheets by greasing them then lining them with parchment paper. Preheat the oven to 350 F.
Scoop the cookies onto the pan in 2-2.5 tablespoon mounds.
Bake the cookies, one tray at a time until they are golden on the edges and the centers don’t look ‘wet’ - about 12 minutes but timing will vary depending on size scooped. If you want flatter cookies, lift the pan slightly and drop it on the counter to flatten.
Out of the oven some of the cookies might look misshapen; while they’re still very warm, I use a deli container (you can also use a large round cookie cutter) to ‘scoot’ the cookie around to make it circular (see video for guidance).
Store the cookies in an airtight container, they’ll last up to 3 days at room temperature. If you’d like longer storage, freeze them.