How to cook eye of round roast?
Eye of round is an excellent cut for braising. You can braise it in stock or red wine. An example recipe would be the classic Beef Bourguignon.

It's also a perfect candidate for slow-cooking in a crock pot, as well as simply roasted in the oven. If cooking it in the oven, use a thermometer and don't cook it past medium. An overnight marinade can be used prior to roasting for additional flavor as well.