Tie boneless prime rib with butcher's twine every 2-3 inches to create uniform thickness. Mix steak seasoning with olive oil to form wet rub. Coat entire roast.
In disposable foil pan, combine thinly sliced onions, rosemary, thyme, beef broth, red wine, and butter.
Preheat smoker to 275°F. Place drip pan on lower grate. Position prime rib on grate above drip pan. Smoke until internal temperature reaches 125-130°F for medium-rare, approximately 2-3 hours.
Remove prime rib and rest 15 minutes loosely tented with foil. Strain drip pan contents, reserving onions separately. Transfer liquid to saucepan and reduce by half over medium heat, about 8-12 minutes, to make au jus.
Make horseradish mayo by mixing mayo, horseradish, and chives. Remove twine from rested prime rib and slice thin.
Slice slider buns. Spread horseradish mayo on bottom buns. Layer with 2-3 slices prime rib, red wine onions, and provolone cheese. Top with bun tops.
Place assembled sliders on baking sheet. Warm at 275-300°F for 10 minutes until cheese melts. Serve immediately with au jus for dipping.