Adjust oven rack to middle position and heat oven to 350 degrees. Line rimmed baking sheet with parchment paper. Whisk flour, baking soda, and salt together in bowl.

Whisk brown sugar and granulated sugar together in medium bowl. Whisk in melted butter until combined. Whisk in egg and vanilla until smooth. Using wooden spoon or rubber spatula, gently stir in flour mixture until soft dough forms. Fold in chocolate chips.

Working with 2 tablespoons dough at a time, roll into balls. Evenly space dough balls on prepared sheet. Using bottom of greased drinking glass, flatten dough balls to 1/2-inch thickness.

Bake cookies until edges are set but centers are still soft and puffy, about 13 to 16 minutes, rotating sheet halfway through baking. Let cookies cool on sheet for 5 minutes, then transfer to wire rack. Serve warm or at room temperature.