Preheat oven to 300 degrees and line a baking sheet with oven-safe parchment paper.
Using a stand mixer, cream together softened butter and sugar on medium-high speed until smooth and fluffy, 2-3 minutes.
Reduce the mixer speed to low and slowly add in the flour, ½ cup at a time, until all 4 cups are incorporated.
Remove dough from the mixer and gently press into prepared baking sheet. Gently use your fingers to spread the dough throughout most of the pan leaving it about 1 inch thick.
Bake until lightly browned, 25-30 minutes. Let cool completely.
While shortbread is cooling, place chocolate chips and 2 tablespoons of the coconut oil in a microwave safe bowl and heat until melted, 2-3 minutes, stirring every 45 seconds.
Next, place the peanut butter and the remaining 2 tablespoons of coconut oil in a second microwave safe bowl and heat until melted, about 30-40 seconds.
Once shortbread is completely cooled, slice into strips using a sharp knife or pizza wheel.
Working one at a time, slowly dip shortbread bar into the melted chocolate so that the lower third is evenly coated in chocolate. Place on parchment paper and continue until all shortbread bars are dipped in chocolate.
Next, use a large spoon to carefully drizzle melted peanut butter over the chocolate coated section of each shortbread bar. Let chill 30 minutes in the refrigerator before serving.