Heat grill to medium. Finely dice 1/2 onion. In a large bowl, combine the diced onion, beef, tomato paste, bread crumbs, Cheddar, parsley, egg, 2 teaspoons of the salt, and 1/4 teaspoon of the pepper. Have ready 2 sheets of foil, each 3 feet long, stacked on top of each other. Fold the foil in half, then unfold, so there's a crease in the center. Place the mixture in the center of the right half and shape it into a loaf. Cut the remaining onions into 1-inch wedges. Place the onions and potatoes around the loaf, drizzle with the oil, and season with the remaining salt and pepper. Fold the left side of the foil over the top, and fold all the edges together several times to create a tight seal. Place on grill and cook, turning upside down every 6 to 7 minutes, until the loaf is cooked through and registers 150° F on an instant-read thermometer, about 40 minutes total. Let rest for 10 minutes before slicing.
Tip: If you're grilling the main dish, select sides that can also be cooked outdoors so you don't have to run between stovetop and grill.