Prepare BBQ Smoker or grill for indirect cooking at 250 - 275 degrees F (120 - 140 degrees C). Add pecan wood chunks to hot coals for smoke.
Rub Olive Oil (2 tablespoon) over the surface of the Eye of Round Beef Roast (4 pound) and season with Kosher Salt (1 tablespoon) and Freshly Ground Black Pepper (1 tablespoon) on all sides.
Place the roast on one side of the cooking grate. Toss the Sweet Onion (1) in a half size aluminum pan with Olive Oil (2 teaspoon), Salt and Pepper (to taste). Place the pan on the cooking grate with the roast.
Sweat the onion for 20 minutes stirring half way and add Johnny's French Dip Au Jus Base (8 fluid ounce) and Water (16 fluid ounce). Cover the pan and simmer.
Turn the roast after 30 minutes of smoking to brown both sides. Insert a meat probe thermometer set for an internal temperature of 130 degrees F (55 degrees C) (medium rare).
Continue to cook the roast until it hits target temp and remove from smoker. About 1 hour 15 minutes total cook time.
Rest the roast for 30 minutes before thinly slicing. Place the slices in the jus for serving.
While the roast rests, make the Creamy Horseradish Sauce. Combine Mayonnaise (12 ounce). Creamy Horseradish Sauce (4 ounce), Horseradish (1 teaspoon), Frank's® RedHot® Sauce (1 teaspoon), and Salt and Pepper (1 pinch).
Serve the roast beef on French Roll (to taste) topped with creamy horseradish sauce, Provolone Cheese Slices (to taste) and a bowl of the Au Jus for dipping.