In a large bowl, whisk together the flour, baking soda, cornstarch and salt. Set aside.
Then, in a medium-sized bowl, combine the melted butter and sugars until no lumps remain. Then mix in the egg and egg yolk. Finally, whisk in the vanilla. Pour the wet ingredients into the dry and mix well with a spatula. Finally, fold in the butterscotch chips. Cover the dough and chill for at least two hours. (Do not skip the chilling.)
When the dough has cooled, remove it from the refrigerator. Then preheat your oven to 325 degrees F.
Roll about 2Â tablespoons of the dough into a ball. Roll the balls so that they are taller, instead of wider. This will ensure that the cookies bake up thick. Place the balls on a baking sheet lined with parchment paper or a silicone mat. Add some of your reserved butterscotch chips to the top of each dough ball for looks, if desired. Bake the cookies for 12 - 14 minutes. The cookies may seem soft or underbaked; however they will continue to bake on the cookie sheet. Allow to cool on the cookie sheet for about 10 minutes. Then move them to a wire rick to cool completely.
Once cooled, prepare your white chocolate dip. In a double boiler (a microwave will work as well, melt your chips along with 1 tablespoon of vegetable shorting. Make sure all of the chips have melted and the chocolate is smooth. Dip half of each cookie into the chocolate; then place on wax paper until the chocolate cools and firms.