This recipe is very similar to one posted by Linda's Busy Kitchen on Food.com named "Shirleys Perfect Rare Roast Beef Recipe". This is the way my mom made rare roast beef, and apparently it is also the way Linda's mom made it, because the methods are virtually the same! We used to eat it with ketchup, but now I like it plain with a side of root vegetables. Leftovers make pretty terrific sandwiches.
Bring your roast (chuck, rump, loin, whatever roast you prefer) to room temperature. Preheat oven to 500 degrees. Pat the roast dry. I actually "age" the roast for a day or two unwrapped in the refrigerator to dry the surface of the meat. Season roast if desired, but don't use salt - it draws the juices out and tends to dry the roast during cooking. So it's important to have a preheated oven, and the roast at room temperature, with a dry surface, and no salt. Line a shallow pan with sliced onions, if desired. Place the roast in the pan. Leave uncovered. Cook the roast at 500 degrees for 5 minutes per pound. For example, you would cook a 4 lb roast 20 minutes at 500 degrees. Do not open the oven. Turn the oven off and let the roast sit for an hour. Remove the roast from the oven and let it rest for about 20 minutes. Slice thinly against the grain. Serve with horseradish or mustard, au jus, or just plain. Wonderful with onions and root vegetables such as parsnips, carrots, potatoes, and beets.