Place racks in the upper and lower thirds of the oven and preheat to 375°F
In a small bowl, whisk together the flour, salt, and baking soda. Set aside.
In a large saucepan over medium heat, cook 1/2 cup of butter, stirring often until it foams and turns brown, about 4 minutes.
Pour the browned butter into a large heatproof bowl and let it cool for 1 minute.
Cut the remaining 1/4 cup of butter into small pieces and add to the brown butter
Once the butter is melted, add both sugars and whisk until well mixed and smooth, with no lumps.
Add the egg and egg yolks, then whisk until the sugar dissolves and the mixture is smooth, about 30 seconds.
Whisk in the vanilla extract. Using a rubber spatula, fold the dry ingredients into the butter mixture until just combined and no dry spots remain.
Fold in the chocolate (the dough will be soft but should hold its shape when scooped; if it slumps, stir it back together and let it rest for 5–10 minutes until the flour hydrates)
Using a 1 & 1/2-oz. scoop (3 tbsp), portion out 16 balls of dough and place them on 2 parchment-lined baking sheets.
Bake the cookies for 8–10 minutes until they are deep golden brown and firm around the edges, rotating the sheets if needed for even browning.
Let the cookies cool on the baking sheets.