Eye of round steak originates from the beef hindquarter -- a highly-exercised and relatively tough muscle group -- and requires chemical tenderization, a moist-heat cooking environment or mechanical tenderization to achieve palatability. Marinades that contain an acidic liquid, such as red wine, and a tenderizing agent, such as papain, relax tightly-coiled muscle fibers and break apart chains of amino acids that contribute to the toughness of meat. Glancing blows from a meat mallet breaks up connective tissue and flattens meat, resulting in shorter cooking times. Braising uses relatively low heat and moisture to melt away the binding connective tissues that make round steak tough.
Make the base for the tenderizing marinade. Add 3 tbsp. olive oil, 3 tsp. papain and 1/4 cup red wine or other acidic liquid to a mixing bowl and mix well.
Add flavoring elements to the marinade base. Seasonings commonly used in beef marinades include Worcestershire sauce, cayenne pepper sauce, fresh minced garlic, liquid smoke, sage, rosemary, oregano, freshly-ground black pepper and kosher salt. Mix thoroughly and store in an airtight, non-aluminum storage container.
Place the round steak in a sealable, plastic storage bag. Add approximately 1/2 cup of marinade to the bag for every pound of eye of round. Remove as much air as possible from the bag and place on a plate in the refrigerator. Marinate for six hours to 24 hours, depending on the weight of the steak. Turn the bag over halfway through the marinating process. Discard the marinade after use. Wipe the excess marinade from the steak and pat it dry before cooking.
Place the round steak on a cutting board and cover with a piece of plastic food wrap larger than the board. Anchor the plastic wrap by placing the top and bottom edges under the cutting board.
Tap the meat using the cross-hatched side of a meat mallet. Strike the meat with glancing blows -- direct, high-impact strikes cause uneven spots and holes in the meat.
Use the flush end of the mallet head to flatten meat if necessary. Occasionally, a butcher slices the round steak unevenly, or there might be imperfections in the meat that result in raised knots on its surface. Lightly tapping the meat with the flat side of the mallet will give the meat a uniform width that facilitates even cooking.
Preheat the oven to 325 degrees Fahrenheit. Add 1 tbsp. olive oil to a sauté pan and place over high heat. When the oil shimmers, add the round steak and sear on both sides. Searing the round steak creates a Maillard reaction, a chemical process that causes meat to brown and caramelize by altering the properties of amino acids.
Add the round steak to a baking dish. Add enough braising liquid to reach halfway up the sides of the steak. Common braising liquids include red wine, water and beef stock.
Cover the baking dish tightly with aluminum foil and place in the oven. Cook until fork tender, or approximately one hour and 30 minutes to two hours. Relatively low cooking temperatures and a moist-heat environment facilitate the breakdown of cartilage, elastin and other connective tissues that contribute to round steak's toughness.