Mix salt, pepper, thyme, rosemary and olive oil together to make paste. Rub paste evenly onto roast.
Let roast sit at room temperature for 30 minutes. Preheat the grill/rotisserie to high (about 450°F).
Skewer meat in middle of roast with spit. Place spit on rotisserie and close lid. After browning meat (about 20 minutes), turn temperature down to medium (about 275°to 300°F).
Cook approximately 1 hour and 30 minutes, or approximately 25 minutes per pound to cook to medium-rare doneness of 135°F measured by internal meat thermometer in middle of thickest part of roast. To achieve medium doneness, cook to 145°F.
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.