Melt the unsalted butter in a light-colored saucepan over medium heat. Continue cooking, stirring or swirling frequently, until the milk solids turn amber-brown and the butter smells nutty, then promptly transfer it to a heatproof bowl.

Cool the browned butter for 15 to 30 minutes, until it is warm rather than hot. Hot butter can melt the sugars and cook the eggs, which can make the finished cookies greasy or overly flat.

Whisk the cooled browned butter with the brown sugar, granulated sugar, eggs, and vanilla until smooth and well combined. In a separate bowl, whisk together the flour, baking soda, and salt.

Add the dry ingredients to the butter mixture and stir only until no dry flour remains. Fold in the semisweet chocolate chips or chopped chocolate without overmixing the dough.

Scoop the dough into approximately 2-tablespoon portions and arrange them on parchment-lined baking sheets. Chill the scooped dough for at least 30 minutes; chilling for 1 to 2 hours produces thicker cookies.

Bake at 350°F (175°C) for 10 to 12 minutes, until the edges are set and lightly golden while the centers still look slightly soft. Let the cookies cool on the baking sheet for 5 to 10 minutes before transferring them to a rack, and sprinkle with flaky sea salt while warm if desired.