01 - Build a campfire with hot coals or preheat an outdoor grill to medium-high heat.
02 - In a large bowl, combine ground beef with salt, pepper, garlic powder, and smoked paprika. Mix gently, then divide into 4 equal portions and shape into flat, even patties.
03 - Lay out 4 large sheets of heavy-duty aluminum foil. Drizzle the center of each sheet with olive oil to prevent sticking.
04 - Arrange sliced potatoes in the center of each foil sheet. Layer 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 yellow mustard.
06 - Fold the foil tightly around the contents, crimping the edges to form fully sealed packets that trap steam during cooking.
07 - Place the sealed packets directly on hot coals or grill grates. Cook for 25-30 minutes, flipping once halfway through, until the potatoes are tender and the beef is cooked through to an internal temperature of 160°F.
08 - Carefully open each packet, watching for hot steam. Place a slice of cheddar cheese over each patty and reseal the foil. Let rest for 1-2 minutes until the cheese melts.
09 - Serve hot directly from the packet or transfer to hamburger buns. Offer additional ketchup, mustard, or mayonnaise on the side.