Freeze the candy bars until hard, at least 1 hour; cut into 1/4-inch pieces and keep frozen until ready to use.
Whisk the flour, baking soda, baking powder and fine salt in a medium bowl. Beat the butter, brown sugar and granulated sugar in a large bowl with a mixer on medium speed until light and creamy, about 3 minutes. Add the egg and vanilla and beat until combined. Reduce the mixer speed to low and gradually beat in the flour mixture until incorporated. Stir in the frozen chocolate pieces.
Line 2 baking sheets with parchment paper. Arrange scoops of dough (about 2 tablespoons per cookie) about 2 inches apart on the baking sheets. Refrigerate until cold, at least 1 hour or overnight.
Position racks in the upper and lower thirds of the oven and preheat to 375 degrees F. Sprinkle the cookies with sea salt. Bake, switching the pans halfway through, until light golden, 10 to 12 minutes. Let cool completely on the baking sheets.