Brown the butter: Cut butter into pieces. Place in light-colored saucepan over medium heat. Stir frequently until it foams, subsides, and turns amber with brown specks. Immediately pour into heatproof bowl. Cool 10-15 minutes. Add 1 tablespoon melted butter.
Mix wet: In a large bowl, combine cooled brown butter, brown sugar, and granulated sugar. Whisk until glossy. Add egg and vanilla. Whisk until smooth.
Mix dry: In a separate bowl, whisk together flour, baking soda, and salt.
Combine: Pour dry into wet. Fold until just combined. Add chocolate chips. Fold until evenly distributed. Do not overmix.
Chill (optional): Cover and refrigerate 1-2 hours. Optional, without chilling, dough spreads a little more but works fine.
Fill mold: Preheat oven to 175°C (350°F). Roll dough into 1-tablespoon balls. Place 5 balls in the mold in a checkerboard pattern (alternating squares).
Bake: Bake 8-10 minutes until edges are golden. Cool completely in the mold for 10-15 minutes.
Melt chocolate: Melt chocolate chips in a heatproof bowl over a double boiler or in the microwave in 30-second bursts, stirring until smooth.
Add chocolate: Pour melted chocolate over cooled cookies, filling empty squares and covering tops. Tap mold to remove air bubbles. Add sea salt if desired.
Freeze: Freeze 20-30 minutes until solid. Pop bars out of the mold and enjoy! Store in the fridge or freezer.