Whisk together the flour, baking soda and salt in a bowl.
In a stand mixer, fitted with the paddle attachment, cream the butter on medium speed until light and fluffy, then add the shortening until evenly mixed in. Add sugars and beat for 3 minutes on medium speed. Mix in vanilla. Add eggs one at a time and mix on medium-low speed just until incorporated. Add flour and mix just until incorporated. Mix in chocolate. Scoop cookie dough using a portion scoop, I used a 3 ounce (83g) scoop. You can make the cookies larger or smaller, but it will effect the baking time.
Refrigerate the dough for at least 30 minutes if you are in a yank, but they improve if you let them sit for 24-36 hours. Resting will make them taste better, be more uniform in shape and color nicely when they bake. After they are chilled you can bake them or freeze the dough balls for later baking.
To bake: Heat oven to 375°F.
Bake 6 chilled cookie balls, evenly spaced on a sheet pan in the middle of the oven for about 12-15 minutes. Sprinkle with flaky sea salt while the cookies are baking. Do it when they are almost set but not done baking.
Allow the cookies to cool slightly on the pan and then remove to a cooling rack.