Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.

Cut potatoes into ½-inch-thick wedges.

Toss potatoes on a baking sheet with a large drizzle of oil, salt, and pepper. Roast on top rack until browned and tender, 20-25 minutes.

While potatoes are roasting, thinly slice tomato into rounds.

Drain pickle, reserving ½ tsp pickle juice (1 tsp for 4 servings) in a small bowl.

Add mayonnaise, ketchup, and mustard to bowl with pickle juice; whisk until combined.

In a large bowl, combine beef*, ½ tsp salt (1 tsp for 4 servings), and pepper.

Form into two patties (four patties for 4), each slightly wider than a burger bun.

Heat a drizzle of oil in a large 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; cover pan until cheese melts.

Remove pan from heat; set aside, covered, until ready to serve.

While patties cook, halve and toast buns until golden.

Spread cut sides of buns with sauce (save some for serving); fill buns with patties, sliced tomato, and as many pickle slices as you like.

Divide burgers between plates; serve with potato wedges and remaining sauce on the side for dipping.