Melt the unsalted butter in a saucepan over medium heat until it foams and turns amber with nutty brown bits, then remove from heat and let cool slightly until warm, about 5 to 10 minutes. The butter should look golden and smell toasted as the foam subsides.

Whisk the light brown sugar and granulated sugar into the warm browned butter until smooth and glossy, about 30 to 60 seconds. You should see no dry sugar patches.

Whisk in the egg and vanilla extract until the mixture looks uniform and slightly thick, about 30 seconds. Stop as soon as streaks disappear.

Whisk the all-purpose flour, baking soda, and fine salt in a bowl until evenly combined, about 15 to 20 seconds. The dry mix should look speckled from the baking soda.

Add the dry ingredients to the wet ingredients and mix just until no dry flour remains, about 20 to 30 seconds. The dough should be soft and slightly sticky.

Fold in the dark chocolate chips until evenly distributed, about 20 to 30 seconds. You should see chips throughout the dough, not just on top.

Preheat the oven to 350°F and line a sheet pan with parchment, then portion dough balls about 2 tbsp each with space between them. The dough balls should keep their shape when placed.

Bake until the edges are golden and the centers look slightly underdone, about 10 to 12 minutes. A faint set should form around the perimeter while the middle stays soft.

Cool on the sheet pan for 5 minutes, then transfer cookies to a rack to cool until the bottoms are set, about 10 to 15 minutes. The cookies will continue to set as they cool.