1 to 1 1/4 pounds new red potatoes halved
2 tablespoons Tuscan extra-virgin olive oil plus more for drizzling
Kosher or sea salt
Freshly ground pepper
Fleur de sel for sprinkling
Prepare a medium-hot fire in a charcoal grill or preheat a gas grill on medium-high.
Poke the potato halves once with the tines of a fork. Place the potatoes in a bowl and toss them with the 2 tablespoons olive oil. Season lightly with kosher salt and pepper.
To create a cool zone, bank the coals to one side of the grill or turn off one of the burners. Oil the grill grate. Arrange the potatoes, cut side down, directly over the medium-hot fire, cover, and grill until dark brown grill marks appear, about 4 minutes. Turn cut side up, re-cover, and grill for 4 minutes longer. Move the potatoes to the cooler part of the grill, cover, and grill until tender when pierced with a knife, about 10 minutes longer.
Transfer the potatoes to a serving bowl. Drizzle with olive oil, sprinkle with fleur de sel, and toss. Serve immediately, or keep warm until ready to serve.