In a mixing bowl, beat together the softened butter, garlic cloves, smoked paprika, dried rosemary, kosher salt and black pepper until it becomes one cohesive mixture.
Rub the butter mixture all over the prime rib, including the sides, so that it's well-covered like so.
Place the prime rib on a 225-degree smoker with a water pan and a drip pan underneath. Insert a leave-in meat thermometer in the center of the roast. Close the lid.
When the internal temperature reaches 105-110 degrees F, remove the roast and increase heat to 400-450 degrees F. Place the prime rib back on the smoker to reverse sear and form a crust.
Remove prime rib and let it rest under foil for 20-30 minutes. Carve into slices and serve with horseradish sauce and au jus if desired.
Make your next gathering even more special with this smoked prime rib recipe. Everyone will fall in love with that tender, juicy roast.