GIARDINERIA: Several hours to one day before you prepare the meat, put all the vegetables for the giardineria in a jar. Heat the olive oil, vinegar, and salt in the microwave just until warm. Pour over the vegetables, then put a lid on the jar and store in the refrigerator.
MEAT: Preheat the oven to 350° F/175° C. In the small bowl, stir together the ingredients for the dry rub, then rub the mixture all over the outside of the roast. Stick in the meat thermometer and place the roast on the rack. Roast in the oven until the meat is 140° F/60° C (medium rare). Remove from the oven and allow it to sit for 1 hour before slicing.
AU JUS: In the 6 quart pot, add the beef broth, garlic, oregano, and black pepper.
Using the electric knife or meat slicer, shave the meat as thinly as possible and put the slices into the au jus. Simmer for about 30 minutes. Do not boil the meat.
SWEET PEPPERS: While the meat simmers, put the sliced sweet peppers, broth, water, and oregano in the small sauce pan and heat just to a boil, then drain.
To serve, pile some of the meat onto the sliced rolls, then dip the whole thing into the au jus. Then add some sweet peppers and some of the giardineria. Eat with lots of napkins or paper towels.
Makes 12 to 16 sandwiches, depending on the size rolls you use.