This is something my mom has been in warmer weather since I can remember. I personally never liked potato salads, except for this one. I don't know her original recipe, but the one I've put together is very similar to it, with a few adjustments (she used just red potatoes). Not exactly something that was difficult to veganize, but very tasty. This tastes better a day or two after it's made because the vegetables absorb the flavors when you let it sit in the fridge.
How to Make It:
Boil 2 or 3 lbs. of baby potatoes (various colors like white, red, and purple, or just red) for about 16 minutes. While doing this cook several handfuls of fresh greenbeans. When vegetables are soft, rinse with cold water and allow to cool. Make dressing using balsamic vinaigrette, lemon juice, dijon mustard, vegan worcestershire sauce, and minced garlic. Chop up some fresh basil. Toss all ingredients together.