Whisk mayo, horseradish, lemon juice, garlic, salt & pepper; mix until well combined.
CAN BE PREPARED & REFRIGERATED UP TO 2 DAYS IN ADVANCE.
Combine seasonings in a bowl; mix well to combine. Pat roast halves dry with a paper towel & rub with 2 tbsp seasoning mixture. Wrap meat tightly with plastic wrap. Refrigerate 24 hours.
Turn all burners to HIGH, cover & heat until hot, about 15 minutes. Leave primary burner on HIGH & turn off all other burners.
Open bottom vent halfway. Light large chimney starter filled with charcoal (about 6 qts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover & open lid vent halfway. Heat grill until hot, about 5 minutes.
4Clean & oil cooking grate (on either grill). Unwrap roasts & place end to end on long side of 18" x 12" sheet of aluminum foil. Loosely fold opposite long side of foil around top of roasts. Place meat on cool part of grill with foil covered side closest to the heat source. Cover & cook until meat registers 100 degrees F., about 45 - 60 minutes.
5Transfer roasts to plate & discard foil.
GAS: Turn all burners to HIGH.
CHARCOAL: Carefully remove cooking grate & light large chimney starter 3/4 full with charcoal (4 1/2 qts). When top coals are partially covered with ash, pour evenly over spent coals. Set cooking grate in place & cover. Heat grill until hot, about 5 minutes.
6Pat roasts dry with paper towels & rub remaining spice mixture. Place meat of hot part of grill. Cook (covered for gas), turning occasionally until charred on all sides & meat registers 120 - 125 degrees F. (for medium rare), about 10 - 20 minutes. Transfer meat to carving board, tent loosely with foil & rest 15 minutes before carving. Slice meat thin against the grain.
7Transfer sliced beef to buns, top with onions & drizzle with sauce. Enjoy!