Preheat oven to 350 degrees. Melt butter in 10-inch cast iron skillet over medium heat and set aside for 5 minutes to cool.
Mix sugars, eggs, and vanilla together in a large bowl until smooth. Stir in the melted butter. Do not wipe out the skillet. Mix the flour, salt, and baking soda together in a separate bowl. Add the dry ingredients into the wet ingredients and mix well with a wooden spoon until dough is blended. Be careful not to over mix. Stir in the chocolate chips.
Spread the dough into the cast iron skillet and smooth the top of the dough. Bake on center rack for 40 minutes until edges are lightly brown and crisp and center is still soft. Cool on a wire rack for 15 minutes. Cut into wedges and serve.