Start with preparing a horseradish aioli by adding mayonnaise, garlic puree, lemon juice, horseradish, salt and white pepper into a small bowl. Whisk together until smooth and creamy.
Select smaller onion rings and fry in oil that is between 350-375° until golden brown. Take sliced ciabatta bun and place onto a hot griddle buttered-side-down. Place the prime rib directly onto the griddle and top with Asiago cheese until it begins to soften and prime rib is warmed through.
Remove the toasted bun, spread the aioli and place the onion rings on top one side of bread. Using grill spatula, pick up the prime rib and cheese together and add on top of onion rings. Place second side of bread on top.