Look for the smallest red potatoes you can find, sometimes called B reds or creamer potatoes. If larger potatoes are used, you will need to cut them into smaller pieces so that they will cook quickly.
1½ pounds very small red potatoes, halved
½ cup extra-virgin olive oil
3 tablespoons white wine vinegar
Pinch of sugar
Salt and freshly ground black pepper
1½ cups cherry or grape tomatoes, halved
½ cup firmly packed fresh basil leaves
Cook the potatoes in a saucepan of salted boiling water until just tender, 12 to 15 minutes. While the potatoes are cooking, make the dressing.
In a bowl, combine the oil, vinegar, sugar, and salt and pepper to taste. When the potatoes are cooked, drain them well and toss gently with the dressing. Add the tomatoes and basil, tossing gently to combine. Taste and adjust the seasonings, adding more salt and pepper if needed. Serve warm or at room temperature.