Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper or silpat mats.
In a large microwave-safe bowl, heat the butter until very soft but not completely melted. Stir the sugars into the butter, mashing out any lumps with the back of the spoon; stir until well blended. Stir in the egg, vanilla, salt and baking soda until the mixture is well blended and smooth. Stir in the flour, just until incorporated. Gently stir in 1½ cups of the chocolate chips. If the dough is too soft to shape, stir in up to 2 tablespoons of additional flour to stiffen it slightly.
Shape the dough into 1 to 1½-inch balls, spacing 2-inches apart on the baking sheets. Use the palm of your hand to flatten each ball slightly. Dot additional chocolate chips on the top of each ball of dough.
Bake one sheet at a time until edges have lightly browned and they are not quite firm when pressed in the middle, 10 to 13 minutes. Let stand for 2 minutes or so before transferring them to a cooling rack.