Preheat a grill to medium-high. Grill bread on both sides until lightly toasted; set aside.
In a small bowl, combine the olive oil, 1 tablespoon of the mustard, the oregano, salt, and pepper. Rub evenly onto chicken breasts. Grill chicken for 12 to 14 minutes or until chicken is cooked through (165°F), turning once halfway through cooking.
Reduce grill heat to medium. Spread 4 slices of the bread with the remaining 2 tablespoons mustard. Thinly slice chicken. Layer chicken, apples, and cheese over the mustard on the bread. Top with the remaining bread slices. Wrap each sandwich in foil. Grill sandwiches for about 6 minutes or until cheese is melted, turning once.