Brown the butter: Add the butter to a light-colored saucepan and cook over medium heat, stirring, until the milk solids turn golden and it smells nutty, 3–5 minutes. Transfer to a large mixing bowl and let cool until warm, not hot, 5–7 minutes.
Preheat the oven to 325°F (165°C). Line two baking sheets with parchment paper.
Bloom the cocoa: Whisk the cocoa powder into the warm browned butter until smooth and glossy.
Whisk in the sugars until combined. Beat vigorously for 30 seconds, rest 2 minutes, then whisk again for 30 seconds to help the sugars dissolve slightly for a shiny top.
Whisk in the egg and vanilla until the mixture is thick and satiny.
In a separate bowl, whisk together the flour, baking soda, cornstarch, espresso powder, and salt. Add this dry mixture to the cocoa mixture and stir with a spatula just until no dry spots remain. Let the dough rest 10 minutes to hydrate.
Fold in the chocolate chips, reserving about 2 tablespoons of chips for topping the warm cookies later.
Scoop 2-tablespoon portions (about 40g) and arrange 2 inches apart on the prepared sheets. Lightly flatten the tops with your fingers.
Bake 12–14 minutes, rotating the pan at 8 minutes and rapping it once on the oven rack to encourage crackly tops. Cookies are done when the edges are set and centers look slightly soft.
Immediately dot the hot cookies with the reserved chips. Cool on the sheet for 5 minutes, then move to a rack to finish cooling.