Step 1

Take the eye of round out of the packaging and trim any excess fat present.

Step 2

Rub with a thin layer of cooking oil.

Step 3

Mix all the rub ingredients and thoroughly coat the entire outside of the eye of round roast including the sides with the mixture.

Step 4

Wrap in plastic wrap and place in the refrigerator until ready to put on the grill or smoker.

Step 5

Start or light your smoker and bring the temperature up to 225°F. If using a gas or charcoal grill, only light one side and set the grill up for indirect heat.

Step 6

Add wood to the smoker using either chunks or a smoker box or pellet tube smoker placed over the burners on a gas grill.

Step 7

Place the eye of round roast in the cooking chamber away from any direct heat. Place a temperature probe into the deepest part of the roast.

Step 8

Cook about 2 hours until the internal temperature reaches about 120°F.

Step 9

While the eye of round is smoking you can prepare the horseradish cream sauce if you wish.

Step 10

Combine all the horseradish cream sauce ingredients in a small bowl and mix well to incorporate. Add extra salt as needed.

Step 11

Cover the bowl with plastic wrap and place in the refrigerator to serve with the smoked roast beef later.

Step 12

Prepare to move the eye of round to the hot side of the grill for reverse searing, or, prepare a hot skillet with cooking oil or Grill Grate on a pellet grill to sear the eye of round when it is ready.

Step 13

Once the internal temperature of the smoked eye of round reaches 120°F, move the eye of round beef roast to the selected place for reverse searing. Rotate about 2 minutes on each side until it is fully seared on all edges.

Step 14

Let the smoked eye of round rest on a cutting board, uncovered, for about 20-30 minutes.

Step 15

Using a good meat slicing knife, slice in as thin of slices as possible.

Step 16

Layer on the Brioche Buns, and serve immediately with the horseradish cream sauce.