Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Slice potatoes into 1/2-inch wedges. Halve, peel, and very thinly slice red onion. 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, flipping halfway through, until browned and crispy, 25-30 minutes.

Meanwhile, in a medium bowl, combine pork, Italian Seasoning, remaining Fry Seasoning, and 3/4 tsp salt (11/2 tsp for 4 servings). Form into two 1/2-inch-thick patties (four for 4), slightly wider than burger buns. Season all over with salt and pepper; set aside. Place 2 TBSP butter (3 TBSP for 4) in a small, microwave-safe bowl. Microwave until melted, about 30 seconds. Stir in garlic powder to taste.

Heat a large drizzle of oil in a large pan over medium heat. Add onion and cook, stirring, until softened and lightly browned, about 10 minutes. (TIP: Add a splash of water if onion begins to brown too fast.) Stir in vinegar and 1 tsp sugar (2 tsp for 4 servings); cook until jammy, about 1 minute. Season with salt and pepper. Turn off heat; transfer to a second small bowl. Wash out pan.

Heat another large drizzle of oil in same pan over medium-high heat. Add patties and cook until browned and cooked through, 3-5 minutes per side. Evenly top with mozzarella in the last 2-3 minutes of cooking. (TIP: Cover pan to melt cheese faster.)

Toast buns until golden brown. Spread garlic butter onto cut sides of toasted buns. Fill buns with patties and top with caramelized onion. Divide between plates and serve with oven fries on the side.