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Preheat your smoker to 225 degrees F with a hardwood like oak, hickory, or pecan.
Season the eye of round roast liberally on all sides with the beef seasoning.
Place the roast directly on the grill grates or in a roasting pan, and cook until the internal temperature reaches 120 degrees for rare roast beef.
Remove the roast from the grill and increase the temperature to High (around 450-500 degrees) or preheat a cast iron pan on your stove top to High. Place the roast on the hot grill or pan and sear for 2-3 minutes per side until the roast is nice and dark all around.
Remove the roast from the heat and rest for 10 minutes. Slice thin against the grain and serve. For any leftovers, allow the roast to cool until it stops steaming, then cover and place in the refrigerator until chilled (I leave it overnight). Once chilled through, slice thin and serve on sandwiches.