Whisk together the flour, baking soda, and kosher salt in a bowl; set aside.
In a mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, combine the olive oil, packed light brown sugar, and granulated sugar until evenly moistened.
Add the whole egg and the egg yolk, then beat on high speed for 30–60 seconds until smooth; mix in the vanilla extract.
Add the dry ingredients and mix on low speed until almost incorporated; do not overmix.
Fold in the chopped dark chocolate with a spatula, reserving a small handful to press on top of the dough balls if desired.
Cover the dough tightly with plastic wrap and chill for at least 30 minutes until firm enough to shape, or refrigerate overnight for best flavor.
Preheat the oven to 350°F (175°C) and line a heavy baking sheet with parchment paper.
Scoop the chilled dough into balls (about 2 tablespoons each, a medium #40 scoop) and shape into smooth balls by pressing rather than rolling; place on the prepared sheet with about 2 inches between each.
Optionally press reserved chocolate pieces into the tops of the dough balls and sprinkle with flake sea salt.
Bake for 9–11 minutes, or 11–13 minutes if baking from frozen, until tops are puffed and edges are golden brown.
Immediately after removing from the oven, give the baking sheet a firm but controlled drop onto the oven rack from a few inches to deflate any excess puffiness.
Let cookies cool on the baking sheet for 15 minutes, then transfer to a wire rack to cool completely.