Preheat your oven to 325°F (165°C).
Season the rump roast generously with salt and black pepper on all sides. You can also rub it with the dried thyme and rosemary for added flavor.
In a large ovenproof skillet or Dutch oven, heat the olive oil over medium-high heat. When the oil is hot, add the rump roast and sear it on all sides until it's well-browned. This step helps seal in the juices and adds flavor to the roast. Remove the roast from the skillet and set it aside.
In the same skillet, add the chopped onion, garlic, carrots, and celery. Sauté for about 5 minutes until the vegetables start to soften and the onions become translucent.
If you're using red wine, pour it into the skillet and stir, scraping up any browned bits from the bottom of the pan. Let it simmer for a few minutes to reduce slightly.
Place the seared rump roast back into the skillet on top of the sautéed vegetables.
Add the beef broth to the skillet. It should come up about halfway to the side of the roast. If needed, you can add a bit more water or broth.
Drop in the bay leaves, and season with additional salt and black pepper to taste.
Cover the skillet or Dutch oven with a lid or aluminum foil. Place it in the preheated oven and roast for about 2.5 to 3 hours, or until the roast is fork-tender. You can check for doneness by using a meat thermometer; the internal temperature should reach 145°F (63°C) for medium-rare, or higher if you prefer your roast more well-done.
Once done, remove the roast from the oven and let it rest for 10-15 minutes before slicing. This allows the juices to redistribute, keeping the meat moist and tender.
Slice the rump roast against the grain into thin slices. Serve it with the vegetables and pan juices as a flavorful gravy.
Serve your deliciously tender rump roast with your favorite side dishes, such as mashed potatoes, roasted vegetables, or a fresh salad.