01 - Build a campfire with hot coals or preheat an outdoor grill to medium-high heat.
02 - In a large bowl, combine the ground beef with salt, pepper, garlic powder, and smoked paprika. Mix gently, then divide into 4 equal portions and shape each into a flat patty.
03 - Lay out 4 large sheets of heavy-duty aluminum foil and drizzle the center of each with olive oil.
04 - Arrange sliced potatoes on the oiled center of each foil sheet. Top with red onion, bell pepper, mushrooms, and cherry tomatoes. Season the vegetables with salt and pepper.
05 - Place one seasoned beef patty on top of each vegetable pile. Drizzle each patty with ketchup and mustard.
06 - Fold the foil tightly around the contents to form sealed packets, ensuring no gaps for steam to escape.
07 - Place the sealed packets directly on hot coals or grill grates. Cook for 25 to 30 minutes, flipping once halfway through, until the potatoes are tender and the beef is cooked through.
08 - Carefully open each packet, watching for hot steam. Place a slice of cheddar cheese over each patty, reseal the foil, and let rest for 1 to 2 minutes until the cheese melts.
09 - Serve hot directly from the foil or transfer to hamburger buns with additional condiments as desired.