Beef eye-round is one of those underappreciated cuts; it is very lean, has the same texture as sirloin, but slightly more beefy flavor. It must not pass medium-rare or it will be tough.
(It looks like an expensive tenderloin filet, doesn't it?)This was an easy preparation. I marinated two 2-inch thick steaks overnight in equal parts of white vinegar and olive oil (about 2 tablespoons each). I salted the meat before grilling. 10/10/20 on the grill: 10 minutes per side on high with the cover up, 20 minutes on the cold side of the grill with the opposite burners set on "low", cover down.
The side was a salad of butter lettuce from farmer's market, supermarket vine tomatoes, Willow Hill Farm La Fleurie, and an assortment of olives. All the ingredients tasted so good by themselves, there was no need for any salad dressing.
After a 5 minute rest, the Medallions were sliced. Rare perfection! Dan can eat a whole steak, but I ate only half of mine. Leftovers make a great cold chef's salad.