About 2-3 hours before cooking, inject the roast with Cajun butter. Using a meat injector, inject the roast all over with Cajun butter marinade, using about one full syringe per quarter section. Use the same hole for multiple angles to avoid over-poking the meat. Total amount of injectable marinade should be about 1 cup for a 6-7 pound roast.
Prepare the roasting tray. Place baby potatoes and onions in the bottom of a roasting pan or deep-sided sheet tray, spread out in a single even layer. Set a wire rack on top. This catches the drippings and flavors the potatoes and onions.
Make and apply the Cajun butter. Mix 1 stick of softened butter with 2 tablespoons Cajun seasoning until well combined. Slather the Cajun butter mixture all over the prime rib roast, making sure to coat all sides generously. Place the roast on the wire rack over the vegetables.
Preheat grill or smoker. Heat your pellet grill, charcoal grill, or smoker to about 250°F with your choice of wood or pellets.
Smoke the prime rib. Place the sheet pan with vegetables and prime rib roast on the grill. Close the lid and smoke at 250°F until internal temperature reaches 117-118°F, about 3-4 hours depending on size and grill temperature.
Remove and increase heat. When the roast reaches 117°F, remove the wire rack with the roast from the grill. Increase grill temperature for searing. *NOTE - If the potatoes are not done yet, you can leave the tray with the potatoes and onions on the grill while the grill is heating to a higher temp. Use an instant-read thermometer to check potatoes – they should reach 208-210°F.
Sear the roast. Once the grill is very hot (about 400-450℉), return the prime rib to the grill and sear on all sides until a nice crust forms and internal temp reaches 120°F, about 10-15 minutes total. *NOTE - Removing the Cajun prime rib at 120℉ allows for about 5-6 degrees of carryover cooking for a perfect medium-rare. For a higher doneness, cook to a higher internal temperature, keeping in mind that the carryover cooking could result in about 5-10 degrees more of doneness.
Rest and carve. Remove the Cajun prime rib roast from the grill, and let rest for 15-20 minutes. Cut away the butcher's twine and carve the roast into 1/2" to 1" thick steaks.
Serve immediately. Plate the Cajun prime rib with the Cajun butter potatoes and onions. Drizzle or serve the blue cheese sauce on the side (optional).
Make blue cheese sauce (optional). While the roast is resting, warm heavy cream with mashed roasted garlic in a small saucepan. Add blue cheese and stir until melted.