For the beef, preheat oven to 325°F and bring the meat up to room temperature. Heat a large Dutch oven over high heat with a turn of the pan of EVOO. Pat roast dry, season liberally with Kosher salt and pepper. In the hot oil, brown roast evenly all over and remove. Wipe pan out and reduce heat to medium. Add another 2 turns of the pan EVOO, 2 tablespoons, add chopped onions, garlic and herbs, and stir. Cook 5-6 minutes to soften, add wine to deglaze pan and reduce 5 minutes more. Add stock and tomatoes, and stir. Add the roast back into pot, cover and roast in oven 3-3 1/2 hours to tender. Remove meat and let rest. Strain sauce and return to pot. Turn heat on high and reduce by half, about 10-15 minutes.
Meanwhile, heat 1 tablespoon EVOO in skillet over medium to medium-high heat. Add cubanelle or bell peppers and sliced onion, and season with salt and pepper. Soften 10-15 minutes. Add some of the meat sauce to the onions and peppers to deglaze.
Dip thinly sliced or shredded beef in sauce and stuff the hoagie rolls. Top with cheese, peppers, giardiniera.