Step 1: Set up your grill for indirect grilling and preheat to medium-high.

Step 2: Cut any large potatoes in half or thirds so all the potatoes are the same size, that is, 1 to 1 1/2 inches. Place the potatoes and scallion whites in a disposable aluminum foil pan large enough to hold them in a single layer. Toss with olive oil and season generously with salt and pepper.

Step 3: Place the pan with the potatoes in the center of the grill away from the heat. Add the wood chunks or chips to the coals. Cover the grill. Smoke-roast the potatoes until tender, 40 to 60 minutes. (Insert a bamboo skewer in one of the pieces to test for doneness: it should go in easily.) Stir the potatoes from time to time so they roast evenly. During the last 5 minutes, roast the potatoes directly over the fire.

Step 4: Transfer the potatoes in their foil pan to a wire rack and let cool to room temperature. Place in an attractive mixing bowl and stir in the Huancaína Sauce. Sprinkle with the chopped scallions greens and serve.