Cut 4 (12-inch) square sheets of parchment. Fold each in half, then open parchment and put a fillet on 1 side of crease line. Season fillets with salt and pepper and sprinkle with garlic and oil. Lay basil, tomatoes and scallions evenly across top of each fillet. Close parchment and crease edges together in a narrow fold to seal.
Lay packets on a large baking sheet and bake until puffed and golden, 10 to 15 minutes. To serve, place packets on plates and slice open with a knife, taking care not to get burned by the steam.