Preparing the Rump Roast:
Dry Brine the Rump Roast: Place the roast on a flat baking sheet or rack. Dry the roast and generously coat it with salt on all sides. Let it brine uncovered in the fridge for at least 4 hours or overnight.
Cooking the Rump Roast:
Preheat the Oven: Set your oven to 350°F (177°C).
Sear the Rump Roast: Heat oil in a Dutch oven over medium-high heat. Sear the roast on all sides for 3-4 minutes each until browned.
Deglaze the Pan: Remove the roast and deglaze the pan with water or broth, scraping up any browned bits.
Add Seasonings and Liquid: Stir in the garlic, oregano, basil, garlic powder, onion powder, thyme, fennel seeds, paprika, celery seeds, bay leaves, and mushroom powder. Return the roast to the pot and pour in the beef broth and water.
Slow Cook the Rump Roast: Simmer on the stovetop, then cover and place in the oven for 2-2.5 hours until the meat is fork-tender.
Preparing the Beef for Sandwiches:
Rest and Slice the Beef: Let the cooked roast cool to room temperature, then refrigerate for 4 hours or overnight for easier slicing.
Strain the Liquid: Strain the cooking liquid and refrigerate until ready to use.
Slice the Beef: Slice the chilled beef thinly against the grain using a mandolin or sharp knife.
Assembling the Sandwiches:
Reheat the Cooking Liquid: Heat the strained cooking liquid. Add the sliced beef to the hot liquid and simmer for 10-15 minutes.
Assemble the Sandwiches: Pile the sliced beef onto the Italian rolls and top with giardiniera, sweet peppers, or hot peppers.
Serve: Serve the sandwiches with a side of the reheated cooking liquid for dipping.