Melt the butter in a small saucepan over medium heat, whisking as it foams, until golden brown and nutty, 3–5 minutes. Transfer to a bowl to cool slightly.

Whisk the browned butter with both sugars, vanilla, egg, and yolk until smooth. Add flour, baking soda, baking powder, and fine salt; mix until just combined. Fold in chocolate chips.

Shape dough into balls and place on a parchment-lined baking sheet. Freeze until firm, about 30 minutes.

Preheat the oven to 350°F/175°C. Arrange dough balls spaced apart and bake until edges are set and centers remain soft, 10–12 minutes. Sprinkle with coarse salt and cool completely on the baking sheet.