Place the brown sugar, garlic salt, seasoned salt, seasoned pepper, onion powder, chili powder, ground mustard, paprika, Italian seasoning, and cumin in a small bowl. Stir thoroughly until the seasonings are evenly blended. Reserve this mixture for coating the ribs.
Inspect the underside of each rack and confirm that the membrane has been removed. If it remains attached, loosen one corner, grip it securely, and carefully peel it away.
Coat both surfaces of the ribs generously with the prepared spice mixture. Press the seasoning firmly against the meat so it adheres well.
Pour the chicken broth and red wine vinegar into the Instant Pot. Position the metal trivet inside the pot, then arrange the seasoned rib racks over the trivet. Curve the racks around the interior of the pot if necessary to make them fit.
Lock the lid into position and turn the pressure valve to SEALING. Select the MANUAL setting and pressure-cook the ribs for 25 minutes.
When the cooking cycle finishes, allow the pressure to release naturally until the pot has completely depressurized. This gradual release helps maintain the ribs' tenderness.
After the pressure has fully released and the lid can be opened safely, carefully transfer the cooked ribs to a baking dish lined with foil.
Brush the ribs liberally with the honey barbecue sauce, coating all exposed surfaces.
Place the glazed ribs beneath the oven broiler for 5–6 minutes, or until the barbecue sauce is bubbling and develops a caramelized finish.
Remove the ribs from the oven. If preferred, brush on another layer of barbecue sauce immediately after broiling for a richer and stickier coating.
While the ribs are pressure-cooking, peel the potatoes and cut them into chunks. Transfer them to a large pot or roaster and add enough cold water to cover them.
Stir 2 tablespoons of salt into the water and bring it to a boil over high heat. Cook the potatoes for approximately 15–20 minutes, or until they are easily pierced with a fork.
Drain away most of the cooking water, retaining roughly one-quarter of the water in the pot with the potatoes to assist with mashing.
Mash the hot potatoes with a potato masher. Add the butter, minced garlic, heavy cream or half-and-half, coarse garlic salt, and coarsely ground black pepper.
Mix thoroughly until the butter has melted, the seasonings are evenly incorporated, and the potatoes have developed a creamy consistency.
Cover the potatoes and keep them warm over the lowest stove setting until ready to serve.
Spoon the creamy mashed potatoes onto serving plates and arrange portions of the caramelized barbecue ribs over or alongside them.
Serve additional barbecue sauce on the side if desired. Garlic toast may also be served as an accompaniment.