Make the pot roast: Preheat the oven to 300 degrees F. Liberally sprinkle the entire beef roast with salt and pepper. Heat the vegetable oil in a Dutch oven over medium-high heat. Add the roast and cook until browned and caramelized all over, 3 to 4 minutes per side (reduce the heat if the fat begins to smoke). Transfer to a plate and reduce the heat to medium.
Add the onion to the pot and sauté, stirring occasionally, until just beginning to brown, 8 to 10 minutes. Add the Italian seasoning and red pepper flakes and sauté until fragrant, another minute. Add the garlic and sauté until fragrant, about 30 seconds. Deglaze with the red wine and cook until reduced by half, about 2 minutes. Add the beef stock and thyme and bring to a simmer. Adjust the seasoning of the jus. Return the beef roast to the pot along with any accumulated juices. Cover, place in the oven and cook, turning the roast every 30 minutes, until very tender, 3 1/2 to 4 hours. Transfer the roast to a cutting board and tent with foil. Increase the oven temperature to 350 degrees F.
Strain the jus through a fine-mesh strainer into a bowl and return to the pot. Bring to a simmer and adjust the seasoning if necessary. Once the meat is cooled a bit, pull it apart into smaller chunks; return to the jus and reserve until ready to build the sandwiches.
Meanwhile, cook the peppers: Toss the green bell pepper strips with the olive oil, granulated garlic and some salt and pepper on a baking sheet. Bake, stirring halfway through, until soft, about 20 minutes.
Build the sandwiches: Place some beef on each hoagie roll, then top with the peppers and some giardiniera. Pour the warm jus into a bowl. Take each hoagie and quickly dunk it in the jus. Wrap in parchment for at least a minute to let the juices "settle," then eat away!