In a small bowl, combine basil, oil, and vinegar; set aside.
Slice bread in half lengthwise. Using a spoon, hollow out bottom half, leaving a 1/2-inch-thick shell. In the shell layer half the cheese, all the pastrami, and all the tomatoes. Top with basil mixture; sprinkle with pepper. Top with remaining cheese and bread top. Wrap in heavy foil. Transport in an insulated cooler with ice packs.
Heat over campfire or on the rack of an uncovered grill over medium heat for 20 to 25 minutes or until heated through, turning every 5 minutes. To serve, cut crosswise into four to six slices. Makes 4 to 6 main-dish servings.