Render the beef fat by chopping it into small bits (about the size of peas) with a food processor. Be sure the fat is very cold--it will chop better. If you don't have a food processor, you can chop the fat by hand. Use a sharp knife and cut it as small as you can. Heat up the fat in a sauté pan over medium heat until the bits are browned. Strain the solids from the fat and measure 1/4 cup of fat for the gravy.
Make the beef gravy by combining all of the ingredients, including the beef fat, in a medium saucepan over medium heat. When the mixture begins to boil reduce the heat and simmer for 5 minutes, then turn the heat to low.
Make the sandwiches by heating up the rolls in the hot oven for 3 minutes.
For each sandwich, drop 1/4 pound of sliced beef (separate the slices) into the gravy for 2 minutes. Make sure the gravy isn't boiling. It should be around 180 degrees F. After the beef has soaked in the gravy, use tongs to arrange the beef on a warmed sandwich roll and top with your choice of hot giardiniera or sweet peppers. Or both. Spoon on some extra gravy just before serving.