Whisk together the flour, baking powder, baking soda and salt. Set aside.

Cream the peanut butter and shortening until well blended. Add the sugar and cream until fluffy. Beat in the eggs, one at a time. Then beat in the vanilla.

Add the flour in 3 installments, mixing in slowly. With the last installment, also add the chocolate chips. Mix just until completely blended. Place in the refrigerator for a minimum of 30 minutes--they will bake nicely after 30 minutes, but my best cookies came with the dough that had chilled at least overnight. It can rest in the fridge for up to 3 days.

Preheat the oven to 350 F. Line your cookie sheet or sheets with parchment of silicone.

Scoop fairly large, about 2-inch diameter, balls of cookie dough onto the cookie sheets. Sprinkle coarse salt to taste on each ball of cookie dough. I baked 6 to a pan to give you an idea. Bake for 12-16 minutes, until lightly browned and starting to crack on top. Let cool on sheets for 5 minutes before transferring to cooling rack.