11. Wash potatoes thoroughly. Cut into 1/4-inch thick fries using sharp chef's knife.
22. Soak cut fries in cold water for 30 minutes to remove excess starch. Drain and pat completely dry with paper towels.
33. Caramelize onions: Mince yellow onions finely. Melt butter in cast-iron skillet over medium-low heat. Cook onions slowly, stirring occasionally, until deep golden brown and jammy, about 25 minutes.
44. Prepare sauce: Whisk mayonnaise, ketchup, relish, and vinegar until smooth.
55. Heat peanut oil in heavy-bottomed dutch oven to 375°F. Use candy thermometer for precision.
66. Fry potatoes in small batches, 3-4 minutes until golden and crisp. Drain on wire rack.
77. Combine American and processed cheeses. Melt using double-boiler method.
88. Layer fries, top with melted cheese, caramelized onions, and special sauce.