Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside.
Brown the butter: Melt the butter in a medium saucepan over medium heat, stirring, until it foams and the milk solids turn deep amber, 5–7 minutes. Immediately scrape into a large heatproof bowl and let cool until just warm to the touch, about 10 minutes.
While the butter cools, whisk the dry ingredients in a separate bowl: flour, cocoa, baking soda, fine sea salt, and espresso powder.
Whisk sugars into the warm browned butter until glossy and combined, 30–45 seconds. Add the egg, egg yolk, and vanilla; whisk until the mixture thickens slightly and looks satiny, about 1 minute.
Switch to a flexible spatula and fold the dry ingredients into the wet until no dry streaks remain. Stir in 1 1/4 cups of the chocolate chips, reserving the rest for topping.
Scoop the dough into 2-tablespoon portions (about 40 g each) onto a small parchment-lined tray. Chill the scooped dough until the surface feels firm, 15–20 minutes. This helps control spread and deepens flavor.
Arrange the chilled dough balls on the prepared baking sheets, leaving 2 inches between cookies. Bake 10–12 minutes, rotating pans halfway, until edges are set and centers look slightly underbaked. For crinkly tops, rap the pan firmly against the oven rack at the 8-minute mark.
Right out of the oven, gently press a few of the reserved chocolate chips into each cookie and sprinkle with flaky sea salt. Cool on the sheet for 5 minutes, then transfer to a wire rack to finish cooling.