Heat oven to 375 degrees. Drizzle garlic heads with oil. Wrap tightly in foil and roast until tender, about 40 minutes. Let cool, then squeeze garlic from papery skin and set aside.
Bring stock, potatoes, and roasted garlic to a boil; reduce heat and simmer until potatoes are tender, about 12 minutes. Remove from heat and stir in Parmesan.
Let cool slightly, then puree in a blender until smooth. Season with salt and pepper. Sprinkle with Parmesan and serve with rustic bread.