Slice the potatoes into 1/4 inch fries, if you wish to peel the potatoes, that is up to you. Place the fries in a bowl of cold water.

Heat 1 tablespoon butter in a skillet over medium high heat until shimmering. Add onion and pinch of salt to skillet. Reduce heat to medium low, and cook, tossing and stirring occasionally until onions are well browned, about 15 minutes. One onions begin to sizzle heavily and appear dry, add 1 tablespoon water to skillet and stir. Continue cooking until water evaporates and onions start sizzling. Repeat process, 3 times total.

In a small bowl add the mayo, ketchup, relish, sugar, and vinegar and stir to combine, this is the sauce, set aside.

Remove the potatoes from the water and dry on paper towels. Heat oil to 365 degrees. Add potatoes in batches and fry for 3-4 minutes or until the fries start turning a bit whiter, then remove with slotted spoon and do the next batch. Let potatoes cool. Then refry by put frying the potatoes again in the hot oil fry a second time for 2-3 minutes, or until golden brown.

Place fries on a large plate, cover with slices of Cheddar cheese, then the onions (or whats left of them), and the sauce. Serve.