Preheat oven to 375 degrees F. Line a sheet pan with parchment paper.

In a small saucepan set over medium heat, melt the butter. Continue to cook the butter until it turns golden brown, stirring frequently, about 3 minutes. Remove from heat and let cool for a few minutes.

Pour browned butter into a large bowl and add the sugar, brown sugar, salt and vanilla. Stir with a wooden spoon until combined. Add the egg and egg yolk, stirring for 30 seconds after each. Let batter rest for about 5 minutes, then stir vigorously for about 30 second. Batter should lighten in texture and color.

In a separate bowl, combine the flour and baking soda. Add to the cookie batter all at once and stir until no streaks of flour remain.

Drop dough by rounded tablespoon onto the prepared sheet pan. Bake until cookies turn golden around the edges but centers aren’t completely set, about 9-11 minutes. Let cool 5 minutes on the pan, then transfer to a wire rack to cool completely.