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 large drizzle of oil, salt, and pepper.

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

While potatoes roast, heat a drizzle of oil in a large pan over medium-high heat. Add onion and cook until lightly browned, 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.

While onion cooks, in a second small bowl, combine mayonnaise, half the horseradish paste, half the mustard, and ¼ tsp sugar (all the horseradish paste, all the mustard, and ½ tsp sugar for 4 servings). (Use less horseradish paste if you’re heat-sensitive.)

In a medium bowl, combine beef*, garlic powder, and half the onion powder (all for 4 servings). Form into two patties (four patties for 4), each slightly wider than a burger bun. Season all over with salt and pepper.

Heat a drizzle of oil in pan used for onion over medium-high heat. Add patties; cook to desired doneness, 3-5 minutes per side.

In the last 1-2 minutes of cooking, top each patty with gouda; cover pan to melt cheese.

While patties cook, toast buns until golden brown.

Spread bottom buns with as much horseradish aioli as you like. Fill buns with patties and caramelized onion.

Divide burgers between plates and serve with potato wedges and any remaining horseradish aioli on the side for dipping.