Adjust rack to top position and preheat oven to 450 degrees. Wash and dry produce.

Slice potatoes into ½-inch-thick wedges. Toss on a baking sheet with a drizzle of oil, salt, and pepper. Roast on top rack until lightly browned and tender, 20-25 minutes.

Meanwhile, peel and cut onion into ¼-inch-thick rounds, keeping layers intact. Halve buns.

Heat a drizzle of oil in a large pan over medium-high heat. Add onion and cook until tender and browned at the edges, 2-4 minutes per side. Season with salt and pepper.

Turn off heat; transfer to a plate. Wipe out pan. TIP: The onion slices won’t brown well if they’re not in a single layer. Cook in batches if necessary!

Form beef* into two patties (four patties for 4 servings), each slightly wider than a burger bun. (TIP: Don’t worry if your patties aren’t perfectly round—those irregular edges will turn deliciously crispy!) Season generously with salt and pepper.

Heat a drizzle of oil in pan used for onion over medium-high heat. Add patties and cook to desired doneness, 3-5 minutes per side. (Careful! Oil may spatter.)

In the last 1-2 minutes of cooking, top patties with cheddar and cover pan to melt.

While patties cook, toast buns until golden brown. Spread as much mustard as you like onto cut sides of buns.

Fill buns with griddled onion, patties, and crispy fried onions.

Divide burgers between plates and serve with potato wedges on the side.