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For the rub: Combine all of the ingredients.
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You probably wont need to use all of the rub.
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The rest can be saved for other meats or even potatoes.
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Spread enough rub on the eye round to cover the surface.
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Place the eye round in a rimmed roasting pan, fat side up, and place the pan on the grill.
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Cook the eye round at about 250 degrees F, with the grill closed, for about 4 hours, or until a bark has developed and the drippings have darkened.
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Once the beef is done, take it, still in the pan, off the grill and cover it with aluminum foil.
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Let it sit, covered, for at least 1/2 hour before slicing it thinly.
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For the rolls: Half an hour before the beef is done, combine the ingredients briefly to form a dough in a large bowl.
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Keep the dough in the bowl and cover it with a kitchen towel or plastic wrap.
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Let rise for about 1 hour, or until the dough has doubled.
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Once the dough has risen, preheat the oven to 525 degrees F. Place the dough on a floured countertop.
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Form the dough loosely into a rectangle about 2 inches thick and use a bench scraper to portion the dough into 8 pieces.
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Place the rolls on a baking sheet covered with parchment paper.
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Bake the rolls for about 10 minutes, or until golden brown.
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For the sauce: Once the beef has rested, remove it from the pan and place it on a carving board.
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Tilt the roasting pan upward and let the drippings run into a corner from which you can collect them.
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Once the rolls have gone into the oven, combine the drippings and flour in a nonstick skillet.
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Add the remaining ingredients and cook over low heat, stirring constantly, until the rolls have about a minute left.
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Turn the heat up to high and cook the sauce, still stirring constantly, until it is thick and a line made in it with the spoon holds.
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Remove the sauce from the heat.
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To make the sandwiches, slice the rolls and fill them with slices of beef.
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Depending on how thinly you were able to slice the beef, and how hungry you are, the number of slices will differ.
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I generally think 3 big slices is enough.
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Top each sandwich with some of the sauce.
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Enjoy!
