Preheat an oven to 360°F (180°C). Line 2 heavy baking sheets or sheet pans with parchment paper.
In a medium saucepan over the lowest heat possible, melt the butter, without boiling, so minimal moisture is lost. Stir regularly, until the butter is almost completely melted.
In a bowl, whisk together the flour, baking powder, baking soda, and kosher salt. Set aside.
Pour the melted butter into a large bowl and whisk in the sugars. The mixture may look like it will seize, but it will relax with a few seconds of stirring.
Add the eggs, one at a time, whisking briskly after each addition, but only to combine.
Stir in the vanilla.
Use a wooden spoon or silicone spatula to stir in the dry ingredients.
Once mostly blended, fold the chocolate into the dough until the remaining flour is incorporated, and the dough no longer looks dusty. Do not overmix.
If the dough seems warm or looks overly glossy, refrigerate for 5 minutes. Then roll into balls using 3 tablespoons of dough for each.
Arrange on the prepared pans, leaving 3 inches in between each cookie.
Sprinkle with sea salt if you like.
Bake until the tops are cracked and lightly golden, yet the cookies are still soft at the center, 10 to 12 minutes, rotating the pan halfway through cooking.
Leave the cookies on the sheet pan for 2 minutes, then transfer to a wire rack to cool.