Who needs mayonnaise when you have tomatoes and basil? Cucumbers or carrots take the place of celery for the crunch factor and red onions add just a touch of heat.
Cut a red onion in half and then finely dice one half until you have 1/4 C. Sprinkle red wine vinegar over the onion and let it sit.
Boil a large pot of salted water. Drop potatoes in the water and boil under they are just tender enough that a sharp knife will go through them — but just barely. Drain the potatoes and then fill the pot with cold water.
Chop 1 lb. of ripe tomatoes, place in a bowl and sprinkle with salt.
Meanwhile, manually defoliate 1 bunch of basil and place the leaves in a food processor. Mince 1 clove of garlic and add to the processor along with 1/2 C. olive oil. Puree until relatively smooth, then add half of a small ripe avocado and puree again. Season with salt.
Add the pesto and the marinated onion to the tomatoes and mix with a spatula.
Drain the potatoes again and dice them the size you like.
Dice 1 cucumber or carrot or some of each.
Toss the potatoes and cukes with the pesto mixture. Add 1/2 C. grated parmesan or crumbled feta cheese. Season with salt and vinegar if necessary.