In a large bowl, whisk the oil, vinegar, ¼ cup of the cheese, ¾ teaspoon salt, and ¼ teaspoon pepper until smooth.
Add the celery, scallions, and parsley and toss to combine. Sprinkle with the remaining 2 tablespoons cheese. Set aside.
In a large skillet, combine the turkey and barbecue sauce and cook over medium heat until heated through, 3 to 4 minutes.
Sandwich the turkey mixture in the rolls and serve with the celery salad.