Preheat the oven to 400 degrees F. Place the garlic on a square of aluminum foil and drizzle with the olive oil. Wrap the garlic tightly in the foil and bake until soft, about 30 to 40 minutes. Unwrap the garlic and cool. Gently press the cloves between your thumb and forefinger to release the softened garlic into a small bowl. Set aside.

Bring a large pot of salted water to the boil. Add the potatoes and parsnips and simmer until they are tender, about 20 minutes. Drain the vegetables and force through the medium disk of a food mill or ricer into a bowl, or alternately mash with a potato masher in a large mixing bowl.

Add the garlic cloves, butter, salt and pepper and mix well, and stir in the cream a bit at a time to achieve the desired consistency. Serve immediately, or chill, covered in the refrigerator for up to 2 days, reheating before serving.