Preheat your grill or oven to 400°F.
In a large bowl, combine the ground beef, diced potatoes, sliced carrots, chopped onion, olive oil, garlic powder, onion powder, paprika, salt, and pepper. Mix well until all ingredients are evenly coated.
Cut four large pieces of aluminum foil, about 12 inches long. Divide the mixture evenly among the foil pieces, placing it in the center of each piece.
Fold the sides of the foil over the mixture, then roll up the ends to create a sealed packet. Make sure there are no openings for steam to escape.
Place the foil packets on the grill or in the oven. Cook for about 30-35 minutes, or until the vegetables are tender and the beef is cooked through.
Carefully open the packets (watch out for steam) and serve hot.