01 - Pour vegetable oil into a deep fryer or heavy-bottomed pot to a depth of at least 3 inches. Heat to 350°F over medium-high heat.
02 - Rinse the cut potato fries thoroughly under cold water to remove excess starch. Pat completely dry with paper towels or a clean kitchen towel.
03 - Carefully lower the fries into the hot oil in small batches. Fry for 4–5 minutes until lightly golden and cooked through. Remove with a slotted spoon and drain on paper towels.
04 - Return the blanched fries to the 350°F oil for an additional 2–3 minutes until deeply golden and crispy. Transfer to a fresh paper towel and season immediately with salt.
05 - While the fries cook, melt the butter in a large skillet over medium-low heat. Add the diced onions and stir frequently for 12–15 minutes until deeply browned, soft, and caramelized. Remove from heat and set aside.
06 - In a small mixing bowl, whisk together the mayonnaise, ketchup, yellow mustard, sweet pickle relish, white vinegar, sugar, and paprika until smooth and fully combined. Refrigerate until ready to use.
07 - Arrange the crispy fries in an even layer on a baking tray. Lay cheese slices over the top and place under the broiler for 1–2 minutes until the cheese is fully melted and bubbling.
08 - Scatter the caramelized onions generously over the melted cheese. Drizzle with the special sauce and serve immediately while hot.