Preheat oven to 400°F.
Place the tomatoes on a sheet tray and drizzle with EVOO. Season with salt and pepper, and toss with thyme and oregano. Roast in the oven for 10 minutes or until slumped.
Heat a large, nonstick pan over medium-low heat. Add the butter and melt. Add the onions and bay leaf, and cook until caramel in color, about 30 minutes. Season the onions with salt and pepper.
Heat a large, cast-iron griddle over high heat. Once the griddle is super-hot, add some canola oil then immediately add the sliced beef and season with a big pinch of salt and pepper. Cook until the meat is just slightly browned, about 2-4 minutes. Arrange the meat on the griddle into a long strip similar in width to the rolls. Top meat with tomatoes, balsamic drizzle and provolone. Using a long spatula, scoop 1/4 of the meat onto each roll. Top with onions, giardiniera, and Italian-flavored potato chips.