Start by melting unsalted butter in a medium saucepan over medium heat. Continuously stir the butter as it melts, allowing it to bubble and foam until it turns a golden brown color with a nutty aroma, about 5-7 minutes. Once browned, remove it from heat and let it cool slightly before moving to the next step.

In a large mixing bowl, combine the browned butter with dark brown sugar and white sugar. Using a hand mixer or whisk, beat the mixture together until it is smooth and creamy, which should take about 1-2 minutes. Then, add in an egg and continue mixing until well incorporated and the mixture is glossy.

In a separate bowl, whisk together all-purpose flour, espresso powder, baking soda, and flaky sea salt. This mixture will create the dry base for your brown butter espresso chocolate chip cookies. Ensure there are no lumps by sifting if necessary, and then set this bowl aside while you prepare to combine the mixtures.

Gradually add the dry ingredient mixture into the wet ingredients while mixing on low speed or folding with a spatula. Combine until just incorporated, being careful not to overmix; you want a thick, slightly sticky dough that embodies the flavors of espresso chocolate chip cookies.

Gently fold in dark chocolate chunks into the cookie dough, ensuring they are evenly distributed throughout. Use a spatula to carefully incorporate them without breaking the chocolate or the texture of the dough. This step adds a rich and decadent element to your cookies.

Using a cookie scoop or spoon, drop generous portions of cookie dough onto a baking sheet lined with parchment paper, spaced about 2 inches apart. For thicker cookies with enhanced flavors, chill the dough in the refrigerator for at least 30-60 minutes before baking, adding a bit more structured chewiness to your espresso chocolate chip cookies.

Preheat your oven to 350°F (175°C). Once ready, place the chilled cookie dough in the oven and bake for 10-12 minutes or until the edges are just golden brown while the centers remain soft. Keep an eye on them as they bake, looking for that perfect, slightly underbaked center.

After baking, remove the cookies from the oven and let them cool on the baking sheet for 5 minutes. Then, carefully transfer them to a wire rack to cool completely. This will allow the cookies to finish setting up while maintaining their chewy center, making them irresistible!