Preheat oven to 350°F (175°C). Lightly grease a 10-inch cast iron skillet with a thin film of softened butter.

Brown the butter: Melt the 3/4 cup butter in a light-colored saucepan over medium heat. Swirl frequently as it melts, foams, and crackles. After 4 to 5 minutes, golden brown flecks (toasted milk solids) will form at the bottom with an irresistible nutty aroma. Immediately pour into a large mixing bowl (scraping all the browned bits) and let cool for 10 minutes until warm, not hot.

Add the packed dark brown sugar and granulated sugar to the warm brown butter. Whisk vigorously for 1 to 2 minutes until glossy and smooth.

Whisk in the whole egg, extra egg yolk, and vanilla extract until the mixture turns pale, thick, and ribbons off the whisk.

Sprinkle the flour, baking soda, and fine sea salt over the wet ingredients. Fold gently with a rubber spatula just until no dry flour pockets remain (do not overmix). Gently fold in 3/4 of the chopped chocolate chunks and chips, reserving a handful for the top.

Press the cookie dough evenly into the prepared cast iron skillet. Scatter the reserved chocolate chunks across the top and gently press them into the surface. Sprinkle with half of the flaky sea salt.

Bake for 18 to 22 minutes until the edges are golden brown and set, but the center is still soft and slightly puffed. Do not overbake; it will continue setting in the hot cast iron pan!

Remove from the oven, dust immediately with remaining flaky Maldon sea salt, and let cool for 5 minutes. Crown with generous scoops of cold vanilla bean ice cream and dig in with spoons!