Preheat oven to 250°F (120°C)
Heat oil in a cast-iron skillet over low heat. Add chopped onions and a pinch of salt. Stirring occasionally, heat until they are soft and golden. 30-40 minutes.
While onions caramelize, move onto the beef. Line a small baking pan with aluminum foil and add a couple of splashes of cooking spray. Place the prime rib on the pan and cover with foil. Warm in the oven for 10-15 minutes, until beef is warmed through.
Remove prime rib from oven and carve into thin slices
Slice ciabatta bread lengthwise at a 45-degree angle into halves. Arrange provolone slices on one-half of each sandwich.
Toast ciabatta under the broiler on high heat for 2-3 minutes, until the provolone starts to melt.
Remove bread from the broiler and arrange each sandwich with warmed prime rib slices, caramelized onions, arugula, and horseradish mustard. Serve and enjoy immediately.