Prepare the grill for direct heat cooking. Heat your grill to about 325-350°F with a direct heat cooking zone. *We used a Weber kettle charcoal grill, with the hot coals in an even layer for even cooking.
Season the beef ribs. While the grill is heating, evenly season all sides of the ribs with salt and pepper. Allow the seasoned ribs to rest for about 20-30 minutes for the seasoning to penetrate the meat.
Grill the ribs. Place the ribs on the grill grates directly over the heat source with the bone-side down. Close the grill lid and cook for about 20 minutes. Then open the lid, flip the ribs to the next side, close the lid, and cook for an additional 20 minutes. Continue cooking the ribs, flipping every 20 minutes, until they reach an internal temperature of about 190-195℉ (about 1 hour and 45 minutes for us). *TIP - When flipping, you can also move the ribs to different areas on the grill as needed to ensure they cook evenly.
Make the barbecue sauce glaze. While the ribs are cooking, add all of the glaze ingredients (barbecue sauce, mustard, apple cider vinegar, and hot sauce) to an aluminum foil pan. Mix together well. Set aside.
Glaze the beef ribs. Once your beef ribs reach an internal temperature of about 195°F, use a basting brush to glaze with the barbecue sauce mixture. Then continue cooking until the internal temperature reaches about 200-203°F, or until tender.
Rest the beef party ribs in the foil pan with the remaining sauce. When the ribs are done cooking, toss in the remaining barbecue sauce in the foil pan. Then place the foil pan of ribs on the grill, close all the grill vents, and close the grill lid. As the grill calms down and the temperature drops, the residual heat will finish the cooking process, and your beef party ribs can rest on the grill.
Serve your beef back party ribs. Serve the beef ribs after they have rested for about 45 minutes and the internal temperature has dropped to about 150°F.