Brown butter: Cut butter into pieces. Place in light-colored saucepan over medium heat. Stir frequently as it melts, foams, then subsides. When small brown specks appear and butter smells nutty and turns amber, remove from heat immediately. Pour into heatproof bowl, scraping all brown bits. Cool 10-15 minutes.
Mix wet: In a mixing bowl, combine cooled brown butter, brown sugar, and granulated sugar. Whisk vigorously until combined and glossy. Add egg and vanilla, whisk until smooth and mixture lightens slightly.
Mix dry: In a separate bowl, whisk together flour, baking soda, and salt.
Combine: Pour dry ingredients into wet. Fold with spatula until just combined, a few flour streaks is okay. Add chocolate chips and fold until evenly distributed. Do not overmix.
Chill: Portion dough into 50g balls (about 3 tablespoons each). Place on parchment-lined tray. Cover and refrigerate 1-2 hours. Freezer works well too.
Preheat and prep: When ready to bake, preheat oven to 175°C (350°F). Line baking sheet with parchment.
Bake: Place chilled dough balls on prepared sheet, 8-10 cm apart. Bake 12 minutes until edges golden brown and centers look slightly soft.
Cool: Let cookies rest on baking sheet 5-10 minutes. Transfer to wire rack to cool completely.