Melt the butter in a saucepan over medium heat until fully liquefied and browned to a deep amber color, with the milk solids caramelized and a rich, nutty aroma released. Remove from the heat and pour the browned butter into a mixing bowl. Stir in the instant espresso powder until fully dissolved, then set the mixture aside to cool. In a separate bowl, whisk together the all-purpose flour, cornstarch, baking soda, and sea salt, then set aside. Once the butter mixture has cooled slightly, beat it together with the brown sugar and granulated sugar until thoroughly combined. Add the room temperature egg, egg yolk, and vanilla extract, beating until smooth and creamy. Gently mix in the dry ingredients just until no streaks of flour remain, being careful not to overmix. Fold in the chopped chocolate pieces until evenly distributed throughout the dough. Scoop the dough into balls about 2 tablespoons each and place them on a tray or plate, then chill in the refrigerator for at least one hour or preferably overnight, up to three days. When ready to bake, preheat your oven to 350°F and line two baking sheets with parchment paper. Arrange the chilled cookie dough balls on the prepared sheets, spacing them about 2 inches apart. Bake for 8 to 10 minutes, or until the edges are golden brown and the centers are just set. Let the cookies rest on the baking sheet for one minute before transferring them to a wire rack to cool completely. While still warm, sprinkle the tops with flaky sea salt for added flavor and texture.