Take the rump roast out of the refrigerator about 2 hours prior to cooking to bring it closer to room temperature, but ensure it is not left out for longer.
Using a sharp knife, carefully create three slits that are 2 to 3 inches deep on one side of the roast. Into each slit, insert a clove of garlic along with some sea salt and pepper. Turn the roast over and repeat the process, adding garlic, salt, and pepper into the cuts. Rub the remaining salt and pepper evenly over the entire surface of the roast.
Preheat your oven to 275°F.
In an oven-safe skillet, melt the salted butter over medium-high heat. Sear the roast on all sides until a golden-brown crust forms, which should take about 15 minutes. Once browned, transfer the roast to a plate. Pour the beef broth and red wine into the skillet to deglaze the pan, scraping up any flavorful bits from the bottom.
Return the roast to the pan, arranging the sliced onion and rosemary sprigs around it.
Roast in the preheated oven until the internal temperature reaches 115°F, which should take approximately 12 to 15 minutes per pound of meat (around 48 minutes to 1 hour for a 4-pound roast).
Once done, place the roast on a cutting board, loosely tent it with foil, and let it rest for 20 minutes. The temperature should rise to 130°F for medium-rare or 125°F for rare, making it perfect for serving.