In a food processor, combine the softened butter, minced garlic, rosemary, thyme, and a pinch of steak seasoning. Blend until smooth to create the garlic herb compound butter.

Season the prime rib on all sides with steak seasoning (about 1 teaspoon per pound), then generously coat the entire roast with the compound butter. Place on a raised rack.

Fill a foil pan with the shaved red onions, beef broth, garlic clove, rosemary sprig, thyme sprig, and Worcestershire sauce. This pan catches all the drippings during the cook.

Preheat the smoker to 275°F with applewood. Place the foil pan on the grate and position the prime rib directly above it. Smoke until the internal temperature reaches 125°F, about 2 to 3 hours depending on the size of the roast.

Remove the roast and rest for 15 to 20 minutes. Carryover cooking brings the internal temperature to roughly 130°F for medium-rare.

Strain the liquid from the foil pan through a fine mesh strainer. Reserve the au jus for dipping and set the caramelized onions aside for the sandwich build.

In a bowl, combine the mayonnaise, grated garlic, lemon juice, horseradish, and parsley. Mix until smooth and refrigerate until ready to use.

Using a meat slicer, shave the rested prime rib into very thin slices. Without a slicer, chill the roast 20 to 30 minutes first, then slice as thin as possible with a long, sharp knife using smooth full-length strokes.

Toast the ciabatta buns until golden and crispy. Spread garlic horseradish aioli on each bottom bun, pile on the shaved prime rib, and top with the caramelized red onions from the drip pan.

Add 2 slices of provolone per sandwich and broil for 1 to 2 minutes until the cheese is melted, bubbly, and lightly browned. Spread more aioli on the top bun, close the sandwich, and serve immediately with warm au jus for dipping.