1 small sweet onion, such as Vidalia, coarsely chopped
1 cucumber—peeled, halved lengthwise, seeded and cut into 1/2-inch dice
1/4 cup extra-virgin olive oil
Basil leaves, torn if large
Halve the tomatoes lengthwise and peel them using a swivel-bladed vegetable peeler in a back-and-forth motion. Cut the tomatoes into bite-size, irregular wedges, discarding any runny seeds. In a small bowl, toss the tomatoes with a pinch of salt and the vinegar. Let the tomatoes stand for up to 30 minutes.
In a mini food processor, pulse the onion until minced; be careful not to overprocess the onion into a puree.
Shortly before serving, transfer the tomato wedges to a medium bowl with a slotted spoon; discard the tomato juices. Add the cucumber and onion and toss, then season with salt. Add the olive oil and toss to coat, then add the basil and toss once more. Serve promptly.