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 until they are cool enough to handle, about 30 minutes. Meanwhile, combine olive oil, butter, garlic and rosemary in a small mixing bowl and mix until well combined. Add a couple of cranks of salt and pepper each to the mixture and stir.

Line a baking sheet with foil or parchment paper and gently press each potato with the palm of your hand until split open and flattened to about 1-inch thickness (don't press too flat or potatoes will break apart).

Brush potato tops with butter and oil mixture; top with cranks of salt and pepper.

MAKE AHEAD: This can be made 2 to 3hours ahead. Let stand at room temperature, or the night before, then cover with plastic wrap and store in refrigerator.

Prepare grill to medium-high heat. Place potatoes, oiled side down, on grill. Brush backsides with oil mixture. Cook until crisp and beginning to color, about 5 minutes per side. Serve warm.