Using an electric mixer on medium speed, beat the butter, brown sugar, and peanut butter until thoroughly mixed. Add the cornstarch, vanilla, and salt, and mix well.
Reduce mixer speed to low. Gradually add the flour mixture, and mix just until combined. Stir in the peanuts. The mixture will be crumbly but should hold together when pinched.
Transfer the dough to a sheet of parchment paper. Use your hands to press the dough together and pat out to a rectangle about 11"x 14".
Transfer the parchment paper and dough all at once to a rimmed baking sheet.
Bake 18 to 22 minutes or until golden brown.
To make the topping:
Sprinkle the chocolate chips and peanut butter chips over the top of the baked shortbread.
Use an offset spatula to spread the chips over the top of the shortbread until they're melted and smooth. Sprinkle the peanuts over the top.
Allow the topping to set before cutting into bars.*
Notes
*These can be cut in several different ways. I prefer squares, but don't forget about triangles, rectangles, and more.