Preheat oven to 375 degrees F.
In a large mixing bowl, add browned butter (make sure it's cooled enough so that it doesn't scramble your eggs), egg, egg yolk, brown sugar, sugar, and vanilla. Whisk to combine.
To the same bowl, add flour, salt, and baking powder. Stir to fully combine and a dough is formed. Fold in chocolate chunks and walnuts (if using), but do not over-mix.
Press the dough evenly into a greased 10" cast iron skillet. Sprinkle a few more chocolate chunks and walnuts onto the top of the cookie dough.
Bake at 375 degrees F for 20 - 25 minutes, or until the top of the cookie is golden brown and the center reaches 200 degrees F.
Remove from the oven and sprinkle with flaky sea salt if desired. Cool slightly. Serve warm with a heaping scoop of vanilla ice cream!