Carefully remove membrane from back of baby back ribs with a sharp knife, if necessary.
Combine the paprika, brown sugar, salt, garlic powder, chili powder, and black pepper in a bowl. Season the ribs on both sides with the dry rub.
Add water to Instant Pot and insert the trivet. Place the seasoned ribs on top of the insert. (Do not stack them flat on top of each other).
Lock the Instant Pot lid into place and turn the pressure valve to sealing. Press the pressure cooker button and adjust the time to 30 minutes.
Once cooking time is complete, do a quick release by turning the sealing valve to the venting position.
Line a large, rimmed baking sheet with parchment paper or a silicon mat. Preheat the broiler to high.
Transfer ribs to prepared baking sheet. Brush ribs with a generous amount of BBQ sauce on each side.
Broil the ribs for 5 minutes or until bubbly and beginning to char. Remove from oven and cool slightly. Serve immediately with extra BBQ sauce for dipping.
Notes
If you'd prefer to grill the ribs outside instead, preheat your grill to 400 degrees and place the ribs over direct flames for 3-5 minutes to char.