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 until evenly seasoned, then divide into 4 equal portions. Shape each portion into a flat, even patty.
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 thinly sliced potatoes in the center of each foil sheet. Layer red onion, bell pepper, mushrooms, and halved cherry tomatoes on top. Season the vegetables generously with salt and pepper.
05 - Place one seasoned beef patty on top of each vegetable stack. Drizzle each patty with ketchup and yellow mustard.
06 - Fold the aluminum foil tightly around the contents, crimping the edges securely to form sealed packets that trap steam during cooking.
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 fork-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 to 2 minutes until the cheese melts.
09 - Serve hot directly from the foil or transfer onto hamburger buns with additional ketchup, mustard, or mayonnaise as desired.