Melt the butter gently over low heat, then remove from heat and let cool for 10 minutes. Do not brown the butter for this recipe. Also, if you have a microwave-safe mixing bowl you can melt the butter directly in the bowl.
Meanwhile, mix together flour, cornstarch, baking soda and salt. Set aside.
Beat together cool melted butter and sugars in a large bowl using a handheld mixer.
Add egg and beat with mixer until mixture lightens in color. By hand, stir in the oil (or tahini) and vanilla until blended. Stir in the flour mixture just until blended, then stir in chips.
Scoop dough with a large or medium size cookie scoop onto a plate or small tray lined with plastic wrap. You should get 10 or 11 large cookies or 21 medium size cookies. Bake immediately if you have to, or chill. Cookies will hold their shape better when baked with chilled dough.
Cover dough with plastic wrap and chill overnight.
Preheat oven to 375°F. Line 2 large baking sheets with parchment or wax paper or skip this step until after you have chilled the dough.
Bake, 1 sheet at a time, until golden, 12 to 15 minutes (less time if making them small). Transfer cookies to a rack to cool and continue making cookies in same manner using cooled baking sheets.