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I have never smoked an eye of round, but I have roasted quite a few. They are pretty lean, I would use your favorite rub then wrap in bacon. From there I would suggest cooking it to medium rare and slicing.
Also agree the this hunk of lean meat is not idea for smoking unless you are using the smoke for flavor.
Cooks Illustrated had a recipe for eye of round that has gotten very good reviews. It finishes in a 225* oven but uses an overnight salting and a pan searing before finishing in the oven. Don't know why you couldn't use the smoker to first almost cold smoke to get some smoke flavor going then sear and finish in the smoker at 225 with lots of smoke at the end. Not sure you would get a lot of penetration of smoke but that would be okay if you could even get a hint of smoke for this roast.
I agree totally. I use eye of round when I do chili cook-offs. Not much fat to trim off. I would smoke it for a few hours to get the flavor and then transfer to oven with some stock, potatoes, onions carrots.
You could, I suppose, inject it for added moisture and just cook it all the way on the smoker.
I smoked some...they're good if you keep it low and slow. Take it off at 140F internal. Spritz it with OJ during smoking....I always use hickory and they come out real nice. Of course it is a lean piece of meat, so slice it thin. You won't be disappointed.
Smoked one and it turned out okay. Had a nice flavor but was on the tough side. Would like to try again. Was thinking of foiling up next time half way through or finishing up in the slow cooker, with ground slab bacon or salt pork. Maybe a hunk on the rack above before. As Rivet suggested, planning on slicing thin is a good idea.
I smoked my eye of round yesterday to about 150 degrees. Then, I put it in the crockpot with onions, carrots, water, and the juice from the pan I carried it in the house with. SO GOOD. I will make a thin gravy to warm it up for a little added moisture. It was a wee bit dry, but oh so good.