Preheat the oven to 350 degrees F. Grease a 10” cast iron skillet with softened butter.
In a medium bowl, combine the flour, baking powder, and salt. Set aside.
Brown the butter: In a small saucepan, add 297g (21 tbsp) of salted butter and place over medium heat. As the butter melts, stir it with a rubber spatula to encourage even cooking. Once the butter has fully melted, it will alternate between rapid large bubbles and gentle small foamy bubbles. The butter will be ready once it turns a dark golden color and the fat solids have darkened and settled at the bottom of the pan. Immediately pour into a large bowl, scraping out the fat solids at the bottom, and weigh out to 255g (1 cup + 2 tbsp).
To the brown butter, whisk in the sugars, then the eggs, milk, and vanilla until well combined.
Add the dry ingredients and fold with a rubber spatula until just combined.
Lastly, fold in the chocolate chips and crushed candy cane pieces.
Transfer the cookie dough to the prepared skillet and smooth out into an even layer. Top with more chocolate chips, if desired.
Bake the cookie skillet for 40-45 minutes or until evenly golden brown on top.
Allow the cookie skillet to cool for a few minutes, then top with more candy cane pieces and a few scoops of vanilla ice cream, and enjoy!