In a medium bowl, sift together the flour, cornstarch, and baking soda. Set the bowl aside.
Using a stand mixer, or a large mixing bowl and an electric handheld mixer, cream together the butter and cream cheese on medium to medium-high speed, for 1 to 1½ minutes. Using a spatula, scrape down the sides of the mixing bowl.
Add the sugars, salt, and vanilla extract. Beat on medium speed until the butter and sugar mixture for 1½ to 2 minutes. Scrape down the sides of the mixing bowl.
On low speed, add the egg. Mix until no yellow streaks from the eggs are visible. Keep scraping down the sides of the bowl.
Continue the mixer on low speed, and slowly add the flour mixture half a cup at a time just until the flour mixture is well incorporated.
Using a large wooden spoon, stir in the chocolate chunks and mini-chips.
Cover the cookie dough and refrigerate for 1 hour.
Before removing the cookie dough from the refrigerator, preheat the oven to 350°F and line a cookie sheet with parchment paper.
Using a 1½ tablespoon cookie scoop, scoop the cookie dough. Gently roll the dough into a ball and place it on the cookie sheet. Space the dough balls 2 inches apart.
Bake for 10 to 12 minutes.
Allow the cookies to rest on the cookie sheet for 1 to 2 minutes before transferring the cookies to a cooling rack.