Place the butter in a light-colored saucepan over medium heat. Stir frequently as it melts, foams, and begins to brown. Once golden brown bits appear on the bottom and the butter smells rich and nutty, remove it from the heat immediately. Pour it into a heatproof bowl and let cool for about 20 minutes.
In a medium bowl, whisk together the flour, baking soda, baking powder, and salt.
In a large bowl, combine the cooled brown butter with both sugars until smooth.
Whisk in the egg, egg yolk, and vanilla until glossy and fully incorporated.
Gently fold the dry ingredients into the wet ingredients until just combined. Be careful not to overmix.
Fold in the chocolate chips and chopped chocolate.
Cover and chill the dough for at least one hour. Overnight is even better if you have the time.
Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
Scoop about two tablespoons of dough per cookie, spacing them about two inches apart.
Bake for 10 to 12 minutes, until the edges are golden while the centers still appear slightly underbaked.
Sprinkle with flaky sea salt as soon as they come out of the oven. Let them rest on the baking sheet for five minutes before transferring to a wire rack.