Mix cooked turkey, 1/3 cup plus 1 tablespoon mayonnaise, mustard, and red wine vinegar together in a bowl and set aside.
Mix Romaine lettuce, salad greens, celery, red onion, grapes, olive oil, vinegar, sugar, salt, and pepper together in a large pretty serving bowl and toss to blend.
Make a depression in the center of the lettuce mixture in the serving bowl. Mound the chicken mixture in the center and sprinkle with peanuts.