Preheat oven to 350 degrees F. then line cookie sheets with parchment paper.
In large mixing bowl, beat the butter until it is smooth then scrape the sides. Add in the sugar then continue to beat on medium speed until the butter and sugar are combined.
Now, add the 1 egg and the 1 1/2 tsp of vanilla extract to the mixing bowl and mix again until the new ingredients are combined with the butter sugar mixture. Make sure to scrape the sides throughout so that everything gets incorporated correctly.
Now add in the dry ingredients like the flour, baking soda, cornstarch, baking powder, and salt. Mix very slow so that all of the dry ingredients don't come flying out all over the place. Once your dough is about formed, add in your white chocolate chips and your chopped cookie pieces then mix a few moments longer until everything is combined.
Use a small spoon from your kitchen or a small cookie scoop and scoop out about 2ish tablespoons of cookie dough. Either drop the cookie dough from the scoop directly or take the dough out of spoon so that you can gently roll the dough in your hands to create a small ball then smoosh it a little bit onto the cookie sheet, so it is still round but slightly flattened.
Now, it is time to bake! Go ahead and stick the cookies into the oven. They should be done in about 8-10 minutes depending on how your oven cooks. I usually do the minimal amount of time and then check to see if they need to be cooked a few minutes longer. Make sure the edges are crisp looking, but it is okay for the middle to be a little soft. You do not want to overcook or burn these.
Let the cookies cool for 5 minutes then you can transfer to your favorite serving plate for family and friends to enjoy!