Prepare the Chuck Roast:

1. Start by making slits in the chuck roast and insert the garlic cloves into these slits.
2. Season the roast liberally with Famous Dave’s Seasoning. Then, using a syringe, inject it with beef broth until it begins to plump up.
3. Smoke the meat over pre-soaked cherrywood and hickory chips at a consistent temperature for 2 hours.
4. Place the smoked roast and sliced Vidalia onion into a slow cooker.
5. In a bowl, whisk together beef broth, tomato paste, and apple cider vinegar until well combined and pour this mixture over the roast.
6. Set the slow cooker to low and cook for an additional 8 hours.

Caramelize the Onions:

1. In a skillet, heat butter and olive oil over medium-low heat. Add the sliced onion and a pinch of salt, cooking slowly until they are deeply amber and caramelized, about 45 minutes.
2. Deglaze the pan with a splash of beef broth, scrape up any browned bits, and set aside.

Assemble and Cook the Grilled Cheese:

1. Spread about two teaspoons of mayonnaise on one side of each slice of sourdough. On the opposite side of half the slices, spread about 2 tablespoons of plum preserves.
2. Heat a non-stick skillet over medium-low heat.
3. Place the bread, mayonnaise side down, into the pan. On the preserve-spread slices, layer 1/3 cup of the cheese mixture, followed by 1/2 cup of shredded beef, 1/4 cup caramelized onions, and another 1/3 cup of cheese.
4. Top with another slice of bread, preserves side down, and grill until the bread is golden brown and the cheese has melted, flipping once. This should take about 3-4 minutes per side.