In a large bowl, use an electric mixer to cream together the shortening and peanut butter. Add brown sugar, granulated sugar, and vanilla extract. Mix until completely combined. Add eggs; beat until fluffy.
In a separate bowl, sift together flour, salt, baking soda and baking powder. Gradually add the dry ingredients to the peanut butter mixture; mix until thoroughly combined.
Cover the dough and chill in the refrigerator for at least 2 hours.
Preheat oven to 375° F. Line baking sheets with parchment paper or silicone mats.
Place about ½ cup of additional granulated sugar in a shallow bowl. Using a cookie scoop (about 1 ½ tablespoons), roll dough into balls and coat in sugar. Arrange the dough balls 2-3 inches apart on the prepared baking sheets. Gently flatten each ball by using a fork to make a crisscross design. Bake for 8-10 minutes, or just until the cookies are a light golden brown color, the edges are set, but the centers are still slightly soft. Cool on the baking sheets for about 3-5 more minutes, and then transfer to wire racks to cool completely.
Notes
For soft peanut butter cookies, pull the cookies out of the oven when they still look slightly under-baked in the center. They will firm up as they cool, but will remain nice and chewy on the inside.
Chilling the dough for about 2 hours yields the thickest, chewiest peanut butter cookies.
Use a processed peanut butter (like Jif or Skippy) rather than all-natural peanut butter. The processed nut butters do not separate, which yields a better quality cookie.