In a medium bowl, whisk together the flour, kosher salt, baking powder, and baking soda.
In a stand mixer fitted with the paddle attachment, cream the butter on medium speed until light and fluffy, then add the shortening and beat until evenly mixed in. Add the brown sugar, honey, and sour cream, and beat for 3 minutes on medium speed to combine. Mix in the vanilla. Add the egg and yolk one at a time and mix on medium-low speed just until incorporated. Add the flour mixture and mix just until incorporated. Mix in the chocolate.
Scoop the cookie dough using a portion scoop (I used a 3-ounce/83-gram scoop). You can make the cookies larger or smaller, but it will affect the baking time.
Refrigerate the dough for at least 30 minutes if you are in a yank, but the cookies improve if you let them sit for 24 to 36 hours before being baked. 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.
Position a rack in the middle of the oven and preheat the oven to 350°F.
Evenly space 6 chilled cookie balls on a parchment-lined baking sheet and sprinkle with sea salt. Bake until set in the middle and golden brown around the edges, about 15 minutes.
Allow the cookies to cool slightly on the baking sheet and then remove to a wire rack to cool. Repeat with the remaining dough balls.