Combine butter, sugar, and brown sugar with a spoon or an electric mixer on medium speed. Mix until light and fluffy. Mix in egg and vanilla. Stir in flour, baking soda, and salt. Stir in chocolate chips and nuts.
Transfer dough to a 10-inch cast-iron skillet. Spread evenly and smooth top.
Bake 25-30 minutes, or until golden brown and just set in the center. Cool 5 minutes before serving.