Melt the unsalted butter in a light-bottomed saucepan over medium heat. Swirl the pan occasionally as the butter melts, foams, and crackles. After 5 to 6 minutes, the foam subsides and amber-gold specks form at the bottom with a nutty toffee aroma. Immediately pour butter and all browned bits into a heatproof bowl; cool for 15 minutes.

Add the dark brown sugar and granulated sugar to the cooled brown butter. Whisk vigorously for 2 minutes until glossy and well combined.

Whisk in the whole egg, extra egg yolk, and pure vanilla extract. Whisk vigorously for 1 minute until the mixture becomes pale, velvety, and forms ribbons.

In a separate bowl, whisk together the flour, baking soda, and fine sea salt. Add the dry ingredients to the butter mixture, folding with a flexible silicone spatula just until a few flour streaks remain.

Fold in the chopped semi-sweet chocolate chunks and dark chocolate chips, saving a small handful for pressing onto the dough balls before baking.

Cover the dough with plastic wrap and chill in the refrigerator for 30 to 45 minutes to solidify the butter and enhance the deep toffee notes.

Preheat oven to 350°F (175°C). Line two large baking sheets with parchment paper.

Using a large 3-tablespoon cookie scoop, portion mounds of dough onto the prepared sheets, leaving 3 inches of space between cookies. Press reserved chocolate chunks into the tops.

Bake for 10 to 12 minutes until the edges are golden and lightly crackled, while the centers remain soft and slightly underbaked.

Immediately after pulling the sheet from the oven, swirl a large round mug or round cookie cutter over each cookie to form perfect circles. Generously sprinkle with flaky Maldon sea salt.

Let cookies rest on the hot baking sheet for 5 minutes to set, then transfer to a wire cooling rack. Enjoy warm with a glass of cold milk!