Preheat the oven to 350F (180C or 170C on a fan forced oven).
Add the chopped walnuts to a cookie sheet and spread into an even layer.
Bake in the preheated oven for 8-10 minutes or until you can smell a nutty aroma. Be careful not to let the nuts burn. Remove from the oven and leave the oven turned on.
Line cookie sheets with parchment paper for baking the cookies.
In a medium bowl, whisk together the flour, cornstarch, baking powder, baking soda and salt.
In a large bowl beat the butter, brown sugar and granulated sugar until fluffy.
Beat in the egg and vanilla extract. Be sure to scrape down the sides and bottom of the bowl.
With the mixer on a low speed, beat the flour mixture into the butter mixture. Gradually increase the speed until combined. The batter will be thick.
Stir in the toasted walnuts and chocolate chips. I always reserve a few extra chocolate chips for dotting on top of each cookie.
Form the dough into balls with about 3 tablespoons of dough each. You can use a large cookie scoop or a 2 scoops of a medium cookie scoop. You'll get 10-11 very large cookies.
Place cookie dough balls at least 2 inches apart on the lined cookie sheets. Bake 1 cookie sheet at a time in the oven for 10-12 minutes, or until the tops look just set. As one sheet is baking, place any cookie sheets with unbaked dough in the fridge.
Cool baked cookies on the cookie sheet for at least 10 minutes. Optionally, add a few extra chocolate chips on top of each cookie.