Combine kosher salt, brown sugar, chili powder, paprika, garlic powder, cayenne pepper, and black pepper in a small bowl.
Cut rib rack into 4 equal portions; rub all sides each portion with spice mixture.
Pour broth into a multi-functional pressure cooker (such as Instant Pot). Add ribs in a teepee formation. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 30 minutes. Allow 10 to 15 minutes for pressure to build.
Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with aluminum foil.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Transfer ribs to the prepared baking sheet. Brush ribs on all sides with barbecue sauce.
Bake in the preheated oven for 7 minutes. Flip ribs; continue baking until meat easily pulls away from the bones, about 7 minutes more. An instant-read thermometer inserted into center should read 145 degrees F (63 degrees C).
