Preheat the oven to 275 degrees Fahrenheit.
Rub this seasoning mixture all over the rump or chuck roast, then set aside.
Heat the vegetable oil in a large oven-safe pot or Dutch oven over medium-high heat, then sear the seasoned roast on all sides until browned, about 3-4 minutes per side. Remove the roast and set aside.
Add the beef broth, beer or Coke, Worcestershire sauce, and beef bouillon to a large measuring cup, stir to combine, then set aside.
Melt the butter in the pot, then add the onions and sauté for 3 minutes, until they become slightly soft, then add in the garlic and cook for 30 seconds or until fragrant.
Pour in the prepared broth and bring to a simmer, then place the roast and thyme in the pot and cover with the sauce.
Cover the pot with a lid, transfer it to the preheated oven, and let the roast cook for about 3 hours or until tender.
Once the roast is cooked, remove it from the pot and place it on a cutting board to rest for at least 15 minutes.
Slice into thin pieces. (My roast was so tender it was falling apart even after resting for 30 minutes, so do your best with this part.)
Strain the cooking liquid through a fine-mesh sieve to remove any solids- this will be your au jus sauce for dipping, but keep the strained onions for the sandwiches.
Preheat the oven to 375 degrees Fahrenheit.
Slice the rolls in half lengthwise while still keeping them connected, and generously butter both sides before placing them on a baking sheet.
Toast in the oven for 10 minutes.
Place the slices of beef on one side of each roll, and add a portion of caramelized onions to the other side, along with 3 slices of provolone cheese on top of the roast.
Place the baking sheet with the assembled sandwiches into the oven until the cheese is melted and bubbly, about 8-10 minutes.
Serve the sandwiches with au jus served hot in a small bowl on the side.