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.