Step 1

Prepare the Spread: Whisk together mayonnaise, ketchup, relish, sugar, and vinegar in a small bowl until well combined. Cover and set aside until serving.

Step 2

Prepare the Grilled Onions: Heat butter and oil in a large skillet over medium. Add onions and salt; cook, stirring occasionally, until softened and golden brown, about 20 minutes. When skillet starts to become dry, add 1 tablespoon of water. Continue cooking, stirring often, adding more water, 1 tablespoon at a time, as needed, until onions are very soft, deeply browned, and jammy, 10 to 15 more minutes (you may not need to use all the water). Cover and set aside to keep warm.

Step 3

Prepare fries according to package instructions.

Step 4

Divide fries evenly among 4 plates; immediately top with 1 slice cheese, 3 tablespoons grilled onions, and 3 tablespoons spread.