Set the rump roast out about 2 hours before cooking, without leaving it out longer than that. Taking off the refrigerator chill helps the center heat more evenly once the roast enters the oven.
Cut three deep slits, about 2 to 3 inches deep, into each side of the roast with a sharp thin knife, filling them with the garlic cloves and some of the salt and pepper; rub the remaining salt and pepper over the exterior. The garlic should sit well inside the meat, while the seasoned surface should look evenly coated.
Heat the oven to 275 F. A low oven temperature warms the center gradually and limits the thick gray band that can form around overcooked lean beef.
Melt the salted butter in an oven-safe skillet over medium-high heat, brown the roast on every side for about 15 minutes, then transfer it to a plate and pour in the beef broth and dry red wine. The butter will foam and the beef should develop a deep mahogany crust while the liquid releases browned bits from the pan.
Return the roast to the skillet and arrange the sliced onion and rosemary sprigs around it. The onions should sit in the deglazing liquid, where they soften and absorb the savory pan flavor.
Roast until a thermometer placed in the center reads 115 F, allowing about 12 to 15 minutes per pound, or roughly 48 minutes to 1 hour for a 4-pound roast. Begin checking near the earlier end of the range because internal temperature matters more than the clock.
Move the roast to a cutting board, tent it loosely with foil, and rest it for about 20 minutes before serving at 130 F for medium-rare or 125 F for rare. The roast will continue warming as it rests, and the surface should feel relaxed rather than tight when gently pressed.