Place a large skillet over medium heat. Add the oil and onions. Sauté for 10 to 12 minutes stirring regularly, adding the balsamic vinegar halfway through. Once the onions are nicely brown and caramelized, remove from heat.
In a medium bowl, mix together the horseradish, mayo, sour cream and mustard. Set aside.
Set up an assembly station by laying out the roast beef, cheese slices, arugula, sliced tomato, onions, sauce and buns.
Preheat the oven or griddle to 350°F. Brush the buns lightly with olive oil. Then put them in the hot oven or griddle for 2 to 3 minutes.
Spread the horseradish cream sauce onto the bottom buns. Sprinkle on some arugula or greens. Add several slices of roast beef followed by some salt and pepper. Layer on the caramelized onions, cheese, tomatoes and a few more greens. Add the tops of the buns and serve.