Thoroughly wash, scrub and dry the potatoes. Wrap the garlic for the Romesco sauce in aluminum foil
Preheat the grill to medium high
Place one potato on a flat surface. Hold it tightly on both ends with your thumb and index finger. Using a sharp paring knife and starting from one end, cut thin slices, stopping before reaching the bottom (make sure you don't cut all the way through), keeping the cuts as even as possible. Repeat the process with the rest of the potatoes.
Drizzle ½ teaspoon of olive oil over each potatoes, rubbing them very gently so the are well coated. Sprinkle salt and pepper evenly and place them on the grill. Cover and cook for 25 minutes. At the same time, place the foil wrapped garlic in the grill, and remove it after 15 minutes.
Once the garlic is cooked and while the potatoes continue cooking, prepare the Romesco sauce. Combine all the sauce ingredients, including the garlic, in the food processor and pulse until smooth.
Once the potatoes are ready, place them on a serving platter and cover them tightly with aluminum foil, until they’re ready to be served.