In a small bowl, mix mayonnaise, sugar, parmesan cheese, apple cider vinegar, salt, and bacon bits until blended. Set the dressing aside.
In a large bowl, combine the chopped broccoli, cauliflower, celery, and peas.
Pour the dressing over the chopped vegetables and toss to combine.
Cover the bowl and refrigerate for at least 30 minutes.
Just before serving, stir in the peanuts.
Serve.