Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper.
Whisk together flour and baking soda in a bowl.
Melt butter in a saucepan over medium heat. Cook until browned, then transfer to a mixing bowl.
Add granulated sugar, brown sugar, salt, and vanilla to the butter. Mix until smooth.
Beat in the egg and egg yolk until well combined.
Gradually add the flour mixture, mixing until just incorporated.
Fold in chocolate chips and nuts (if using).
Drop dough by tablespoons onto prepared baking sheets, spacing them 2 inches apart.
Bake for 10-12 minutes, until edges are golden but centers are soft.
Cool on baking sheets for 5 minutes, then transfer to wire racks.