A rump roast is often underrated – it has unusually good flavor. If your roast is rated “prime” or “choice,” you can roast it at 325°F (160°C). Figure on 25 to 30 minutes per pound for rare, 28 to 33for medium rare, 31 to 36 minutes for medium, and as long as you want for well done. To be sure – and we suggest everyone should get an instant-read thermometer – cook it until the internal temperature is 120° to 125° for rare, 130° to 140° for medium rare, 145° to 150° for medium, and 155° to 165° for well done. The meat will continue to cook after you take it from the oven; while you let it rest for 20 to 30 minutes, the internal temperature will rise another 10 degrees or so.
If your roast is of lesser quality, it will be too tough if you roast it, so you should braise it. Brown the meat on all sides in a little oil in a Dutch oven or roasting pan. Pour off the fat, add half an inch or so of boiling beef stock to the pan, cover it, and pop it into the oven at 300°F (150°C) for three to four hours. You will probably need to add additional stock as the meat cooks.