Brown butter: Cut butter into pieces. Place in light-colored saucepan over medium heat. Stir frequently until butter foams, then brown specks appear and it smells nutty. Remove from heat immediately. Pour into heatproof bowl, scraping all brown bits. Cool 10 minutes.
Mix wet: In large bowl, combine cooled brown butter, brown sugar, and granulated sugar. Whisk until glossy. Add egg and vanilla, whisk until smooth.
Mix dry: In separate bowl, whisk together flour, baking soda, and salt.
Combine: Add dry ingredients to wet. Mix with spatula until just combined, do not overmix.
Add KitKats: Fold in chopped KitKat chunks (100g) until evenly distributed.
Portion: Use 3-tablespoon scoop (60-70g per cookie). Roll each portion into a tall ball, do not flatten. Place on parchment-lined tray.
Freeze: Freeze dough balls for 1 hour. Do not skip.
Preheat and prep: When ready to bake, preheat oven to 175°C (350°F). Line baking sheet with parchment.
Bake: Place frozen dough balls on prepared sheet, leaving space between them. Bake 10-12 minutes until edges set and lightly golden, centers still soft and puffy.
Shape: Immediately out of oven, use large round cookie cutter to gently swirl around each cookie into a perfect circle. Do not press down.
Cool: Let cookies rest on baking sheet 5 minutes, then transfer to wire rack.
Decorate: Warm Nutella in microwave 10-15 seconds until spreadable. Spoon 1 tsp onto center of each cookie and spread into thin circle, leaving small bare edge. Immediately press chopped KitKat (40g) into Nutella.
Serve: Let topping set a few minutes. Best served slightly warm or at room temperature.
