I wanted to pass on a recommendation for the America's Test Kitchen recipe for roasted eye-of-round. I made it a few days ago and it was fantastic.
The recipe calls for pre-salting the roast for 24 hours, searing it, then cooking it in a 225 degree oven. The results were great. The meat was very tender, tasty and the slow cooking allowed it to be cooked rare/medium rare all the way through, with almost no outer gray layer.
The recipe certainly took time but was idle time. All in, it took about 2 hours for a 2 1/2 lb roast (bought for about $12 in NY).
First I seared it in a cast iron skillet for about 10 minutes. Then it took about 1 to 1 1/4 hours in a 225 degree oven to reach 115 degrees. You then turn the oven off and let the temp rise to 125 for rare/medium rare which took another 20 or so minutes. The only thing I varied from the recipe was using less salt. I used 1 1/2 tsp of kosher salt, mainly due to me misreading the recipe but it seemed to work out fine and the salt really tenderized and added lots of flavor to the meat. After cooking I carved (or tried) thin slices using a Chef's knife. I put the leftover, uncut, piece into the tupperware and make roast beef sandwiches the next day. This time I used an electric knife which made quick work, and very thin, slices. A highly recommended recipe for turning a really inexpensive roast into a great roast beef.
FYI - i also made the horseradish cream sauce to go along with it.