Preheat the oven to 350 degrees F (175 degrees C).
Beat butter in a large bowl using an electric mixer until smooth. Add brown sugar and white sugar; mix until well blended. Add egg and vanilla extract and beat until smooth.
Toss 2 cups plus 2 tablespoon flour, baking soda, and salt together using a fork in a small bowl. Add to the butter mixture in batches, mixing well after each addition. Fold in 1 3/4 cups chocolate chips. Spread batter into an ungreased 9x13-inch baking pan.
Bake in the preheated oven until edges are golden, about 25 minutes. Spread remaining 3/4 cup chocolate chips on top. Return to the oven until chocolate chips are shiny, about 1 minute more. Remove from oven and spread melted chocolate over the top.
