Combine the garlic, oregano, red pepper flakes, thyme, extra virgin olive oil, and a generous pinch of salt and pepper. Split mixture in half. Rub half of the mixture all over the sirloin tip. Marinate at least 30 minutes. Combine the remaining half of the mixture with a quart of water.
Place on roasting pan and transfer to oven, roasting for 20 minutes.
Pour the rub-water mixture into the bottom of the pan. Reduce head to 350°F Return to oven and roast for another 30 minutes or until a meat thermometer reads rare - 130°F.
Transfer to a cutting board to rest and skim fat from the broth.
Very thinly slice the meat, against the grain. Place the sliced meat into the broth. Assemble sandwiches by piling meat onto the buns, topped with giardiniera. Dip in broth before serving.
For the Giardiniera: Combine all ingredients, mix well, and marinate for 24 hours at room temperature.