I have not had Brothers PSal, but have had some compliments on my own take.
I steam or microwave the potatoes after salting and peppering for five minutes under plastic wrap, drain then toss with vinegar and let them absorb the acid.
Toss them after cooling with homemade mayonnaise made with good olive oil, lemon juice, salt and pepper, along with a teaspoon of dijon. The addition of chopped dill fronds is optional.
Toss with fine diced celery, shallot, chopped hard boiled egg and either chives or green onion.
Let rest in frig for at least six hours or overnight.
Retoss before serving.
I don't know if it would be too embarrassing, but have you tried asking someone at Brother's Deli for the recipe? Or perhaps ask them what makes their potato salad so good, any secret ingredient or something. It never hurts to ask.
My other thought is asking one of the home economists (or whatever they're called these days) at Byerly's. They've been very helpful to me with questions in the past.
I picked some up for the 1st there last weekend,so I can see why you want to get the recipe. I bought the blue cheese potato salad.I put it in my top 3 best store/restaurant potato salads in the metro area.I was worried that the blue cheese might be overwhelming,but it was perfectly balanced.i consciously didn't look at the list of ingredients.