To make the filling in the electric pressure cooker:
Heat the oil in the pot of your pressure cooker on sauté. Brown the beef chunks in the hot oil, turning to sear all sides. Don’t crowd the meat cubes in the pan; you may need to do this in batches. Transfer the meat to a bowl.
Add the onion to the drippings in the pan and cook, stirring, until tender. Add the Italian seasoning and cook for another minute. Stir in the beef broth and cook, scraping up any bits on the bottom of the pressure cooker.
Add the meat back in. Stir well to combine.
Secure the cover and close the pressure valve. Set the pressure cooker to manual high pressure for 45 minutes. Release the pressure when the cycle ends. The meat will be tender and shred easily.
To make the filling in the slow cooker:
Heat the oil in a large skillet. Add the beef chunks and brown on all sides to caramelize. Remove the meat to the crock of a slow cooker.
Add the onion to the drippings in the pan and sauté until lightly browned. Stir in the Italian seasoning mix and heat about 1 minute. Add the beef broth and stir, scraping up any browned bits. Transfer the liquid to the slow cooker. Stir to combine.
Cook on low for 6 to 8 hours or on high for 4 hours. Meat should be tender and shred easily.
To assemble the sandwiches:
Slice the rolls lengthwise and toast them well.
Shred the meat with two forks or small tongs. Divide the meat among the rolls. Top with the optional toppings and serve with jus on the side.
To freeze the Italian beef:
Portion the meat into meal-size containers. Seal, label, and chill the meat completely before freezing. To serve: thaw and reheat before assembling the sandwiches.
Nutritional values are approximate and are based on ⅙ of the recipe. Refrigerate leftovers promptly and use within 4 days.Toppings: Italian beef sandwiches are similar to French dip sandwiches in that they are often served with the cooking juices from the meat, sometimes even drenched. The classic version is served with giardiniera, sweet peppers, and/or pepperoncini. Cheese is not traditionally added, though cheddar, Swiss, and mozzarella are sometimes mentioned on menus.To make the giardiniera easier to eat in a sandwich: drain it well and chop the larger chunks of vegetables into more manageable, bite-sized pieces.To make a freezer kit: Prepare the Italian beef as directed. Remove from the pot and divide into meal-size containers, adding the jus. Chill this completely prior to storing it in the freezer alongside a pack of Italian rolls. Wrap the bread well for freezing.