Cook butter in a light-colored saucepan over medium heat for about 8–10 minutes, stirring, until the milk solids are amber and smell nutty. Transfer immediately to a heatproof bowl and cool for 20–30 minutes until barely warm.

Stir both sugars, vanilla, and 2 tablespoons water into the cooled butter. Add eggs and mix until evenly combined.

Whisk flour, baking soda, and salt, then fold into the wet mixture until no dry flour remains and stir in both chip sizes. Cover and refrigerate for 1 hour until firm and scoopable.

Preheat to 350°F and line 2 baking sheets. Divide dough into 24 equal portions, about 2 heaping tablespoons each, placing 12 on each sheet with gaps of about 2 inches.

Bake 1 tray at a time at 350°F for 10–12 minutes per batch until the edges are golden and centers look set. Rest each batch on its sheet for 5 minutes, then transfer to a rack.