In a large bowl beat (with a stand up mixer or hand mixer), the butter, vegetable oil and both sugars. Mix on medium speed for 2-3 minutes until the mixture is creamy.
Scrape down the sides of the bowl and then add in the eggs and vanilla. Continue mixing until thoroughly combined.
In a separate bowl, stir together the flour, cornstarch, baking soda and salt.
Then mix the bowl of dry ingredients into the wet ingredients. We recommend mixing this by hand so that the mixture does not get over mixed.
Next gently stir in the chocolate chips and chopped walnuts.
Then drop the cookie dough onto baking sheets in approximately 1 tablespoon amounts.
Bake for 8-10 minutes until the edges of the cookies are slightly brown. Do not over bake. The cookies may look raw in the middle but they will continue to cook as they set.
Cool on the baking sheet for 5 minutes and then move the cookies to a wire rack to cool completely.
Then the cookies are ready to serve and enjoy!
Notes
Store the leftover cookies in an airtight container or ziplock bag at room temperature for up to 5 days. Keep a slice of bread in the container with the cookies to keep them moist.