To make the vinaigrette, in a small bowl, whisk together the balsamic vinegar, parsley, garlic and pepper. While whisking, slowly add the olive oil. Set aside.
In a large bowl, combine the beans and onion. Pour the vinaigrette over the mixture and toss gently to mix well and coat evenly. Cover and refrigerate until served.
To serve, put 1 lettuce leaf on each plate. Divide the salad among the individual plates and garnish with chopped celery. Serve immediately.