Preheat the oven to 375 degrees . Arrange the bacon on a broiler pan; bake until crisp, 12 to 14 minutes. Let cool, then chop.
In a medium bowl, mix the bacon, Neufchatel, nuts, scallions and nutmeg.
Season the chicken with salt and pepper. In a heavy skillet over medium-high, heat 1 tbsp. EVOO, one turn of the pan. Add the chicken; cook until browned and cooked through, about 3 minutes per side.
In a medium bowl, whisk the lemon juice, vinegar, mustard, honey and the remaining 3 tbsp. EVOO. Toss with the apple, celery, onion and watercress. Season.
Slather the bagel bottoms with the Neufchatel mixture. Top with a cutlet and salad, then add bagel tops.