1Prepare the caramelized onions: Heat 1 tablespoon olive oil and 0.5 tablespoon salted butter in a skillet over medium heat. Add diced white onion and a pinch of salt. Cook, stirring occasionally, until onions are golden and caramelized, about 10-15 minutes. Add 2 tablespoons water to deglaze the pan and cook until water evaporates. Set aside.
2Make the In-N-Out sauce: In a bowl, combine 0.5 cup mayonnaise, 2 tablespoons ketchup, 1 tablespoon relish, 1 tablespoon caramelized onions, 1 teaspoon white vinegar, 0.5 teaspoon salt, 0.5 teaspoon sugar, 0.25 teaspoon paprika, 0.25 teaspoon black pepper, 0.25 teaspoon garlic powder, and 1 teaspoon yellow mustard. Mix well and refrigerate until ready to use.
3Prepare the potatoes: Dice 2 russet potatoes and toss with 2 tablespoons olive oil and 1 tablespoon potato seasoning. Air fry at 400°F (200°C) for 15-18 minutes until crispy and golden.
4Cook the burger beef: In a bowl, mix 1 pound ground beef with 0.5 teaspoon salt, 0.25 teaspoon black pepper, 0.25 teaspoon garlic powder, and 1 tablespoon yellow mustard. Form into 4 patties. Cook in a skillet over medium-high heat for 3-4 minutes per side. Top each patty with a slice of American cheese and let melt.
5Assemble the bowls: Divide the air-fried potatoes among 4 bowls. Top with cooked burger beef, extra caramelized onions, and drizzle with In-N-Out sauce. Serve immediately.