16 small red-skinned and/or white-skinned potatoes (about 2 inches in diameter)
Fresh rosemary leaves
Cook potatoes in large pot of boiling salted water until just tender, about 25 minutes. Using slotted spoon, transfer potatoes to kitchen towel. Cool potatoes to lukewarm, about 20 minutes. Using another towel, gently press each potato until split open and flattened to scant 1-inch thickness (don’t press too flat or potatoes will break apart).
Brush large baking sheet with oil. Transfer potatoes to prepared sheet. Brush potato tops with oil; sprinkle with salt, pepper, and some rosemary leaves. DO AHEAD Can be made 2 hours ahead. Let stand at room temperature.
Prepare barbecue (medium-high heat). Place potatoes, oiled side down, on grill. Brush with oil. Cook until crisp and beginning to color, about 5 minutes per side. Transfer to platter; sprinkle with more rosemary leaves and serve hot.