How to Make It
Combine potatoes, carrots, parsnips, and garlic in a large saucepan. Add broth, and bring to a boil over high. Reduce heat to medium, and simmer until all vegetables are tender, about 30 minutes. Pour through a strainer into a bowl, reserving cooking liquid.
Transfer carrots and 3 of the garlic cloves to a mini food processor. Process until smooth, adding 1 to 2 tablespoons of the cooking liquid as needed, about 30 seconds. Stir in 1 tablespoon of the oil and teaspoon each of the salt and black pepper. Pulse until combined, about 3 times.
Mash potatoes, parsnips, and remaining 9 garlic cloves until smooth, adding cup cooking liquid as needed. Stir in remaining 3 tablespoons oil, teaspoon salt, and teaspoon black pepper. Spoon potato mixture into a large shallow bowl, and dollop with carrot mixture. Use the back of a spoon to swirl mashed carrots into mashed potatoes. Garnish with cracked black pepper.