Preheat oven to 450 degrees. Wash and dry all produce. Cut potatoes into 1/2-inch-thick wedges. Peel and slice half the onion into 1/4-inch-thick rings, keeping them intact (slice whole onion for 4 servings); mince a slice until you have 2 tsp (4 tsp for 4). Thinly slice tomato and pickle into rounds. Finely chop a few pickle slices until you have 1 TBSP (2 TBSP for 4). Mince chili. Halve buns.

Toss potatoes on a baking sheet with a large drizzle of oil, half the Fry Seasoning, salt, and pepper. Roast on top rack until crispy, 20-25 minutes. Meanwhile, in a medium bowl, combine beef, remaining Fry Seasoning, salt (we used 3/4 tsp; 11/2 tsp for 4 servings), and pepper. Form into two patties (four for 4), each slightly wider than a burger bun.

In a small bowl, combine ketchup, chopped pickle, half the sour cream, and up to half the minced onion to taste. Season with salt and pepper. In a separate small bowl, combine cheddar, mayonnaise, remaining sour cream, 1 tsp minced onion (2 tsp for 4 servings), and a pinch of chili to taste. Season with salt and pepper.

Heat a drizzle of oil in a large pan over high heat. Add onion slices in a single layer (try to keep rings intact but don’t worry if some fall apart); season with salt and pepper. Cook until lightly charred, 1-2 minutes per side. Transfer to a plate.

Heat a drizzle of oil in same pan over medium-high heat. Add patties and cook to desired doneness, 3-5 minutes per side. In the last 1-2 minutes of cooking, top each patty with cheddar spread; cover pan until cheese has melted. Place 1 TBSP butter (2 TBSP for 4 servings) in a small microwave-safe bowl; microwave until melted, 30 seconds. Brush onto cut sides of buns. Carefully place buns cut sides up on top rack of oven until toasted, 3-5 minutes.

Fill buns with patties and as much tomato, charred onion, and sliced pickle as you like. Divide between plates with potato wedges. Serve with special sauce and any remaining sliced pickle on the side.