Preheat oven to 350 degrees F (175 degrees C). Line baking sheets with parchment paper.
Beat shortening with brown sugar, white sugar, and vanilla in a bowl until creamy. Add egg; beat until smooth. Add flour, baking soda, and salt; mix until incorporated. Fold in 1 cup peanut butter chips, toffee bits, and peanuts. Drop batter by the rounded tablespoonful about 2 inches apart onto the prepared baking sheets.
Bake cookies in the preheated oven until deep golden brown and just set in the middle, 10 to 12 minutes. Cool on sheet for 3 minutes before transferring to wire racks to cool completely.
Heat remaining peanut butter chips in a microwave-safe bowl in the microwave until melted, about 45 seconds. Drizzle over cooled cookies.