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

Cut potatoes into ½-inch-thick wedges. Halve, peel, and thinly slice onion.

Toss potatoes on a baking sheet with a drizzle of oil and half the Old Bay Seasoning (you’ll use more later). Season lightly with salt and pepper. TIP: No need to season generously—there’s already salt and pepper in the seasoning!

Roast on top rack until browned and crispy, 20-25 minutes.

While potatoes roast, heat a large drizzle of oil in a large, preferably nonstick, pan over medium-high heat. Add onion; cook, stirring occasionally, until browned and softened, 8-10 minutes.

Add 1 tsp sugar (2 tsp for 4 servings) and a splash of water; cook until onion is caramelized and jammy, 2-3 minutes more. Season with salt and pepper.

Turn off heat; transfer to a small bowl.

Meanwhile, in a second small bowl, combine mayonnaise, ketchup, mustard, and as much remaining Old Bay Seasoning as you like. Set aside.

Form beef* into two equal-size balls (four balls for 4 servings); season all over with salt and pepper.

Heat a drizzle of oil in pan used for onion over medium-high heat. Once pan is hot, add beef. Firmly flatten each ball with a spatula to create very thin patties. (TIP: Do so carefully; oil may splatter a bit.) Cook to desired doneness, 3-4 minutes per side. (Don’t worry if the patties aren’t perfectly round—those irregular edges will turn crispy.)

In the last 1-2 minutes of cooking, top patties with cheddar; cover pan to melt cheese. Remove from heat.

While patties cook, halve and toast buns.

Divide buns between plates and fill with patties, caramelized onion, and half the special sauce. Serve burgers with Old Bay fries on the side and remaining special sauce for dipping.