Mix salt, pepper, thyme, rosemary and olive oil together to make paste. Rub paste evenly onto roast.
Let the roast sit at room temperature for 30 minutes. Preheat the grill/rotisserie to high (about 450°F (232°C)).
Skewer the meat in the middle of the roast with the spit. Place the spit on the rotisserie and close the lid. After browning the meat (about 20 minutes), turn the temperature down to medium (about 275°F to 300°F (135°C to 149°C)).
Cook approximately 1 hour and 30 minutes, or approximately 25 minutes per pound, to cook to medium-rare doneness of 135°F (57°C), measured by an internal meat thermometer in the middle of the thickest part of the roast. To achieve medium doneness, cook to 145°F (63°C).
While roast is cooking, prepare Apple Horseradish Sauce. Combine sauce ingredients and season with salt and pepper to taste. Store in refrigerator in covered bowl for up to 3 days. Sauce should be served cold.
When meat is cooked, remove spit from rotisserie and carefully remove meat. Let meat rest on platter or cutting board, loosely covered with foil for 15 minutes before slicing.
Slice roast ⅛-inch thick across grain. Slicing with grain will result in tougher slices.
Layer sandwich ingredients in amounts and order of personal preference. Serve with favorite potato chips or side dish.
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