In a medium saucepan, reheat the short ribs in their sauce until warmed through. Transfer the ribs to a plate and bring the sauce to a boil. Remove from the heat and keep warm.
Light a grill or preheat a grill pan. Lightly brush the grate or grill pan with oil. Grill the onion over the cooler part of the fire until lightly charred, about 5 minutes per side. Transfer to a plate. Grill the ribs over a hot fire until browned, about 45 seconds per side. Transfer to a work surface and cut into thick slices; discard the bones. Cover with foil. Toast the rolls on the grill or in the grill pan.
In a bowl, combine the mayonnaise and horseradish; season with salt and pepper. Spread the rolls with the mayonnaise, top with the onion and short ribs and drizzle with sauce. Serve with the remaining sauce on the side.
These hearty sandwiches call for a beer that will stand up to the horseradish mayonnaise. Try Samuel Adams Boston Ale or Anchor Steam Beer.