Depending your preference, half or quarter The Little Potato Company’s Creamer potatoes. The Boomer Gold Little potatoes are a bit larger, so I suggest quartering them. Place the potatoes in a bowl and toss with 2 teaspoons olive oil, ¼ teaspoon oregano, ¼ teaspoon salt and pepper.
Using 2 pieces of foil per packet (each 12 inches long), form an X by overlapping the foil. Alternatively, use one sheet of heavy duty foil for each packet.
Divide the potato mixture in half and place each half in the middle of each foil packet. Wrap the foil over the potatoes, pinching the foil to seal.
Place the packets on the grill and cook until the potatoes are just tender when pierced with a fork, 15 to 20 minutes.
In a medium bowl, combine the remaining 1 teaspoon olive oil, balsamic vinegar, ¼ teaspoon oregano and ¼ teaspoon salt. Add the salmon fillets and turn to coat.
Remove the packets from the grill and open carefully. For each packet, top each potato portion with a salmon fillet, half of the tomatoes and 2 basil leaves. Reseal the foil and return the packets to the grill. Cook until the salmon is almost cooked through, about 5 minutes.
Remove the packets from the grill again and carefully open. Remove and discard the basil leaves, and top with the bocconcini. Seal and return to the grill, and cook until the cheese is melted, about 2 minutes.