For the horseradish sauce: In a bowl, mix the mayonnaise, sour cream, horseradish, honey and Dijon. Season with salt and pepper.
For the onions: Pour the buttermilk over the onions and let them sit for about 30 minutes.
Heat 3 inches of oil to 350 degrees F in a medium Dutch oven.
Whisk together the flour, cayenne, paprika and some salt and pepper. Remove the onions from the buttermilk and toss them in the flour until thoroughly coated. Fry in batches until the batter is golden, 2 to 3 minutes. Let drain on paper towels and season with salt while hot.
For the sandwich build: On the toasted onion rolls, begin with a slice of Cheddar, pile the meat high, add as many crispy onions as the sandwich will hold and schmear the top bun with a healthy portion of horseradish sauce.