Prep: Preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.
Brown the butter: In a small pan, heat the butter on the stovetop at medium heat. After the butter has melted, the white milk solids will separate out and sizzle. Stir occasionally. The mixture will foam and the milk solids will sink to the bottom of the pan where they'll start to brown quickly. When the milk solids become golden brown and the butter smells nutty, immediately remove it from the heat and pour it into a large mixing bowl. You should end up with 125g of browned butter. If it's less than that, add additional butter to bring it to that amount. Let it cool for about 10 minutes.
Flour mixture: In a medium bowl, stir together the flour, cornstarch, espresso powder, baking powder, baking soda, and salt. Set aside.
Wet ingredients: To the browned butter, add the granulated sugar and brown sugar. Whisk until combined. Add the egg and vanilla extract and whisk again until smooth and thick.
Combine: Add the flour mixture and fold together with a spatula until mostly combined with some flour patches left. Add the chopped chocolate and fold together until just combined.
Scoop cookie dough: Use a 4-tablespoon cookie scooper to scoop the cookie dough onto your lined baking sheet, leaving about 1-2" in between each to account for spreading.
Bake: Bake for about 11-12 minutes or until the edges are set but the cookies are still very soft. 2 minutes before they're finished baking, press a few extra chocolate chunks on top of each cookie (optional). Immediately sprinkle flaky salt on top of the cookies while they're still warm.
Cool: Let the cookies cool on the baking sheet for about 10 minutes before transferring them to a wire rack to cool completely or enjoy warm!