Preheat the oven to 350 degrees F. Line 3 cookie sheets with parchment paper.
Place the shortening, sugars, peanut butter, egg, and vanilla in a large bowl. Use an electric hand mixer to beat these ingredients on medium speed, scraping the sides of the bowl, until all is well-combined.
In a separate bowl, whisk together the flour, baking powder and salt. Add the flour mixture to the peanut butter mixture and beat on low speed until well-combined (1 to 2 minutes). Don't over-mix.
Scoop up a tablespoon of the cookie dough and use your hands to roll it into a ball. Dip the tines of a fork into sugar and press down on each ball of cookie dough, forming a criss-cross pattern on top. Repeat with the rest of the cookie dough, and place the cookies about 1½-inches apart on the cookie sheets.
Bake until the edges of the cookies are lightly browned, 12 to 14 minutes. Cool and eat!