Trim any large pieces of fat from the chuck roast. Season the roast generously on all sides with salt and black pepper.

Heat 1 tbsp olive oil in a large skillet or Dutch oven over medium-high heat. Sear the roast for 3-4 minutes per side until deeply browned. Remove the roast and set aside.

Add the sliced yellow onion to the same skillet, scraping up any browned bits from the bottom. Cook for 5-7 minutes until softened. Add the minced garlic and red pepper flakes, cooking for another minute until fragrant.

Transfer the seared roast and the onion-garlic mixture to your slow cooker. Pour in the beef broth and Italian dressing. Add the dried Italian seasoning, bay leaf, and 1 tsp salt. Stir gently to combine.

Cover and cook on low for 7-8 hours, or on high for 3.5-4 hours, until the beef is fork-tender and easily shreds.

Once cooked, carefully remove the roast from the slow cooker and place it on a cutting board. Using two forks, shred the beef, or for a more authentic 'thinly sliced' style, let the beef cool slightly and then slice it against the grain as thinly as possible with a sharp knife. Discard the bay leaf from the cooking liquid. You can skim off any excess fat from the jus if desired.

Return the shredded/sliced beef to the slow cooker with the cooking liquid (jus). Keep warm on the 'warm' setting while you prepare the chips and rolls, allowing the beef to soak up more flavor.

Wash and peel the Russet potatoes. Using a mandoline slicer, carefully slice the potatoes as thinly as possible (about 1/16-inch thick). Place the slices immediately into a large bowl of cold water to prevent browning and rinse off excess starch. Drain and repeat rinsing a couple of times until the water is clear.

In a large pot, combine 6 cups of water, 1 cup distilled white vinegar, and 1 tbsp salt. Bring to a boil over high heat. Add the potato slices and boil for 5-7 minutes until they are slightly pliable but still firm (not mushy). This pre-cooks them and infuses vinegar flavor.

Drain the potatoes thoroughly in a colander. Spread the potato slices in a single layer over clean kitchen towels or several layers of paper towels. Pat them extremely dry. This step is crucial for crispiness; ensure no moisture remains. You may need to replace towels multiple times. Allow to air dry for at least 30 minutes, or longer if needed.

Preheat your air fryer to 375°F (190°C). Lightly spray the potato slices with vegetable oil or toss with 1-2 tbsp vegetable oil. Work in batches, arranging a single layer of potato slices in the air fryer basket without overlapping.

Air fry for 12-18 minutes, shaking the basket every 4-5 minutes, until the chips are golden brown and crispy. Cooking time may vary significantly between air fryer models and batch sizes. Transfer cooked chips to a wire rack set over a baking sheet to cool.

Once a batch of chips is out, immediately spray them lightly with the reserved 2 tbsp distilled white vinegar using a small spray bottle, then sprinkle generously with fine sea salt while they are still warm. Repeat for all remaining batches.

Preheat oven to 350°F (175°C) or toast Italian rolls on a griddle/pan if desired. Briefly toast the Italian rolls if you like them warm and slightly crispy.

Using tongs, generously fill each roll with the Italian beef from the slow cooker, allowing some of the flavorful jus to drip onto the bread. Top with a spoonful of giardiniera.

Serve the Italian Beef Sandwiches immediately with the freshly made Homemade Salt and Vinegar Chips on the side. Enjoy!