Whisk flour, baking soda, and kosher salt together in a medium bowl.
Combine brown sugar, butter, and white sugar in a large bowl; beat with an electric mixer until light and fluffy, about 2 minutes. Add espresso, egg, and vanilla extract; beat until combined and smooth, about 1 minute more.
Gradually beat in the dry ingredients until just combined, being careful not to overmix the batter. Fold in chocolate chunks. Let chill in the refrigerator for at least 30 minutes.
Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Using a spoon or 1-ounce ice cream scoop, roll chilled dough into 1-inch balls. Place on the prepared baking sheets at least 2 inches apart. Sprinkle each ball with a pinch of flaky salt.
Bake in the preheated oven until just beginning to turn golden brown around the edges, about 10 minutes. Let cool on the trays for 5 minutes. Transfer to a wire rack to cool completely.