Preheat oven to 350 degrees F.
Cream together the butter, white sugar, and brown sugar until smooth. Beat in egg, then stir in the vanilla.
In a medium-sized bowl, whisk together flour, cornstarch, baking soda, and salt.
Gradually add flour mixture to wet ingredients. Stir in chocolate chips. Cover the dough with plastic wrap and chill for 30 minutes.
Scoop dough and drop by large spoonfuls onto parchment lined cookie sheets, placing at least 2" apart.
Bake for 7-8 minutes or until tops are just barely started to turn brown (centers will be soft). The cookies will look under baked at the end of baking time, but that is good, they will cook completely on the cookie sheets.
Remove from the oven and let them sit on cookie sheets for 10 minutes.
If desired, gently press additional chocolate chips into the tops of the warm cookies. Remove them to cooling rack.