Place the potatoes in a saucepan of salted water and bring to a boil.
Cook until just tender when pierced with a fork, about 12 to 15 minutes. Look for the smallest red potatoes you can find, sometimes called B reds or creamer potatoes. If using larger potatoes, cut them into smaller, uniform pieces to ensure they cook quickly and evenly.
While the potatoes are cooking, prepare the dressing.
In a large bowl (the one you'll serve in), whisk together the extra-virgin olive oil, white wine vinegar, pinch of sugar, and salt and pepper to taste.
Once the potatoes are cooked, drain them well. Immediately add the warm potatoes to the bowl with the dressing and toss gently to coat.
Letting the potatoes absorb the dressing while warm is key to a flavorful salad.
Add the halved tomatoes and fresh basil leaves to the bowl.
Toss gently again to combine all the without breaking up the potatoes.
Taste and adjust the seasonings, adding more salt and pepper if needed.
Serve immediately while warm, or let it cool to room temperature.
Don't overcook the potatoes. They should be fork-tender but still hold their shape, not turn to mush.