Place chicken thighs and breasts in the pressure cooker, with 3 cups BBQ sauce. Stir to coat chicken evenly with sauce.
Set Instant Pot on Manual (High) for 15 minutes. Let the pressure release naturally for 10 minutes.
Shred chicken and put back in the pot. The chicken will soak up most the moisture. Add the rest of the BBQ sauce and stir to combine.
Meanwhile, make the Garlic Butter buns by placing buns on a baking sheet, flat side up. Brush buns generously with melted Garlic Butter, then broil 2-3 minutes, until butter is melted and buns are toasted.
