Tolly Ho is located right near University of Kentucky's Campus and prides themselves on serving students delicious and quality food, fast. Cooking Channel made our own version of the "Ho Sauce" for this burger, which tastes frighteningly similar to a very secret sauce put on a certain fast food chain's burger.
Meanwhile, poke the potatoes with a fork and microwave until softened but not completely cooked through, 6 to 8 minutes. When cool enough to handle, peel and discard the skin. Grate the potatoes on the large holes of a box grater. Add the chopped Cheddar, salt, pepper and garlic powder. Stir with a fork to combine everything, and then stir in the flour.
Heat about 3 inches of oil to 350 degrees F in a heavy pot or Dutch oven (or set a countertop fryer to 350 degrees F). Using a tablespoon of potato mixture, form each tot into a squat cylinder about 1 1/2-inches in diameter and 3/4-inch tall. Fry in small batches until golden and crisp on the outside, 1 1/2 to 2 1/2 minutes. Drain on a paper-towel-lined plate or baking sheet and sprinkle with salt while warm. Serve with the burgers, or freeze for later use in self-sealing freezer bags, and reheat in a 375 degree F oven for 7 to 10 minutes.
For the sauce: Mix the mayonnaise with the relish, capers and a pinch each of salt and pepper. Set aside.
For the burger: Divide the meat into 4 equal portions and form into 4-inch patties about 1/4-inch thick. Sprinkle all the burgers with salt and pepper. Heat a large skillet or a griddle over medium-high heat. Add 1 tablespoon of the butter and, when just melted, add the burgers. Cook, turning once, until browned and cooked to medium-well, 2 to 3 minutes on each side.
Meanwhile, spread the buns with the remaining tablespoon of butter and toast in the oven, 3 to 5 minutes.
To build the burgers, evenly spread the sauce on the bottom half of the buns. Evenly top with the shredded lettuce and onion rings. Add a burger patty, ketchup and mustard, and top with the bun. Serve with the Cheddar tots.