In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a stand mixer fitted with the paddle attachment, cream the butter, shortening, granulated and brown sugars, and vanilla on medium speed until creamy, about 3 minutes.
Add the eggs one at a time, beating on medium speed until incorporated. Add the flour mixture all at once and mix until just incorporated. Mix in the chopped chocolate pieces. You may need to give the bowl a couple of swipes with a rubber spatula at the end to make sure the chocolate is evenly distributed.
Line a baking sheet with parchment paper. Scoop the cookie dough using a #20 (3-tablespoon) portion scoop onto the baking sheet. You can make the cookies larger or smaller, but it will affect the baking time.
Refrigerate the dough balls for at least 30 minutes; but if you have the time, they improve if you let them sit for 24 to 36 hours. After they are chilled, you can bake them or freeze the dough balls for baking later.