Craft the Tangy Spread: In a small bowl, simply whisk together the mayonnaise, ketchup, sweet pickle relish, sugar, and white vinegar until everything is beautifully combined. Cover it and set it aside; this delicious sauce will be ready when your fries are.
Caramelize the Sweet Onions: Heat the butter and canola oil in a large skillet over medium heat. Add your chopped onions and a sprinkle of kosher salt. Cook, stirring occasionally, until the onions become wonderfully soft and golden brown, which usually takes about 20 minutes. As the skillet starts to get dry, add 1 tablespoon of water. Continue cooking and stirring frequently, adding more water, one tablespoon at a time, whenever needed, until the onions are incredibly soft, deeply browned, and have a lovely jam-like consistency. This extra step takes about 10 to 15 more minutes. Cover the skillet to keep these sweet gems warm.
Perfect Your Crispy Fries: Prepare your frozen shoestring potato fries according to the package instructions. This often means baking them in the oven or using an air fryer for a wonderfully crispy finish.
Assemble and Enjoy! Once your fries are hot and crispy, divide them evenly among four plates. Immediately top each portion with a slice of American cheese (the heat from the fries will help it melt beautifully), then spoon about 3 tablespoons of your sweet grilled onions over the cheese, and finish with a generous drizzle of about 3 tablespoons of your homemade tangy spread. Serve right away and savor every bite!