Preheat the oven to 350°F.
Melt the butter in a medium skillet over medium heat. Cook 4-5 minutes, or until the butter gets foamy and starts to turn brown. Remove the butter from the heat and let it cool slightly.
In a large bowl or the bowl of a stand mixer, mix together the brown butter, brown sugar, and sugar. Add the egg, egg yolk, and vanilla extract, and mix until combined.
Add the flour, baking soda, and salt, and mix to form a soft dough. Gently fold in the chocolate chips. Scoop the dough onto the prepared baking sheet using a large cookie scoop (I like to use a 3 tablespoon scoop). Add more chocolate chips on top.
Sprinkle each cookie with sea salt. Bake 12-13 minutes, or until very lightly browned around the edges. The middle of the cookies should still be soft. Let cool on the baking sheet for 5-10 minutes, then remove to cooling rack.