Preheat the grill to 375°F.
Place the meat in a bowl or shallow platter. Drizzle with olive oil and sprinkle with salt, pepper and the rosemary. Make sure to coat both sides. Let sit at room temperature for 30 minutes.
Cut off the root ends of the onion. Slice into ½ inch thick slices and drizzle with EVOO and sprinkle with salt and pepper. Set aside.
Cut the rolls in half and drizzle with EVOO as well.
When the grill is up to heat start by grilling the onions, they take the longest. Grill 8-10 minutes per side. Remove and place in a bowl.
Next grill the bread, 2-3 minutes per side until golden brown and crispy. Set aside until needed.
Lastly grill the meat, 4-5 minutes per side for medium rare. While the meat grills make the mustard sauce. Combine the mustard and horseradish cream sauce in a bowl and mix together.
Remove the meat from the grill and let sit 5 minutes before slicing. Slice the meat against the natural grain on a thin bias.
To assemble the sandwiches slather some of the sauce on the inside of the top and bottom roll. On the bottom bun place a piece or two of the cheese followed by a few pieces of steak, grilled onions, arugula and then place on the top bun. Continue with remaining rolls and meat.
Serve warm or room temperature.
Recipe Courtesy of Megan Mitchell