For vinaigrette, whisk oil, vinegar, garlic, honey, mustard, oregano, salt and pepper in small bowl until well blended.
For each sandwich, drizzle 1 tablespoon vinaigrette over bottom half of bread. Layer with arugula, tomato slices, roasted peppers, cheese slices, additional arugula and basil. Drizzle with 1 tablespoon dressing; replace top half of bread.
