Preheat the oven to 350°.
Combine the white cake mix, cornstarch and all purpose flour in a large bowl. Whisk the ingredients together to combine. Add the softened butter, shortening, eggs and salt to the dry mixture and cream together using a hand held {or stand} mixer. The dough will be a nice thick consistency.
Using a medium cookie scoop {or about 2 tablespoons of dough} get a mound of dough. Add a peanut butter cup to the middle and press down into the dough. Scoop another mound of dough and place on top of the peanut butter cup. Using your hands, bring the two cookie dough mounds together around the peanut butter cup, being sure to seal edges.
Place on a baking sheet, lined with a silicone mat {or parchment paper} and continue making cookies until all of the dough is gone {should have 12 VERY large cookies}. Bake for 10-13 minutes, or until the edges are set and the middle of the cookie is just beginning to set and barely brown. They may look slightly under-baked but let them cool completely on a cookie sheet and they will firm up as they cool.
Once cookies have cooled completely, melt peanut butter and chocolate in separate bowls in the microwave. I like to start with 30 seconds, stir and add more time if needed. Both should be smooth and thin. Using a spoon or fork drizzle both peanut butter and chocolate over the cookies. Allow the chocolate to set up.