Preheat oven to 350 degrees F. Place garlic head in a 6 oz custard cup or small baking dish and drizzle with oil. Bake, uncovered, until garlic is soft and fragrant, about 40 minutes.
Meanwhile, place the diced potatoes into a large saucepan. Add cold water to the pan until the potatoes are covered by at least an inch of water. Add some salt to the water.
Bring the water to a boil over high heat. Reduce the heat to low, cover and simmer for 15 to 20 minutes, or until potatoes are fork tender. Drain potatoes.