I think the special part is that there is no mayo. I make a similar salad, very useful for Pot Luck, since there is not mayo to fret. Here's what I do (Original called for "balsamic vinegar" but I found the color a problem for me):
Asparagus Parmesan Potato Salad
2 pounds red potatoes
1 bunch asparagus
½ medium red bell pepper (seeded & chopped)
2 tablespoons fresh parsley (washed, patted dry, chopped fine & packed into spoon)
3 tablespoons fresh basil (washed, patted dry & chopped)
½ cup fresh lemon juice (approx. 2 lemons worth)
¼ cup extra virgin olive oil
¼ teaspoon paprika
1 tablespoon white balsamic vinegar
4 ounces shredded Parmesan cheese (or to taste)
Place red potatoes in large pot, add water to cover. Bring pot to boil & cook until potatoes are tender but not mushy (about 20-30 minutes). (Or microwave to cook & then cool & chill.)
Cut asparagus into 1-inch pieces and steam until crisp tender.
Cool potatoes completely. Peel potatoes (if desired) & dice.
Place cooled potatoes & asparagus in large mixing bowl. Add the red pepper, parsley & basil.
Whisk lemon juice, olive oil, paprika & balsamic vinegar in a small bowl. Pout over potato mixture & toss well. Season with Parmesan cheese, salt & pepper to taste.