Preheat a grill to medium high. Combine the beef, egg, panko, 2 tablespoons barbecue sauce, 3/4 teaspoon salt and a few grinds of pepper in a large bowl. Add the scallions, reserving 2 tablespoons of the greens for topping. Mix well with your hands.
Tear off four 20-inch-long sheets of foil and lightly coat with cooking spray. Toss the potatoes, carrots and parsnips with the olive oil, thyme and a big pinch each of salt and pepper in a large bowl. Divide the vegetables evenly among the prepared foil sheets, piling them on one side of the foil. Clear a spot in the middle of the vegetables for the meatloaf.
Divide the meat mixture into 4 pieces and shape each into a 3-by-4-inch mini meatloaf on the foil. Fold the foil over the meatloaf and vegetables; fold in the edges to form a packet.
Grill the foil packets, 10 minutes, then flip and continue grilling until the vegetables are tender and the meatloaves are cooked through, 5 to 8 more minutes. Carefully open the packets and brush the tops and sides of the meatloaves with the remaining 1/4 cup barbecue sauce. Sprinkle with the reserved scallion greens.
Brush the barbecue sauce on the meatloaves after grilling — otherwise it might get too dark on the grill.