Preheat oven to 400 degrees Fahrenheit. Trim ends off garlic head. Place each on piece of aluminum foil large enough to fully enclose head of garlic. Drizzle one tablespoon of the oil over garlic. Enclose each head with foil. Place on one side of aluminum- foil-lined baking sheet.

In large bowl, combine potatoes, two tablespoons of oil, thyme, salt and pepper. Transfer to baking sheet. Bake in center of preheated oven for about 45 minutes or until potatoes and garlic are tender

Heat remaining tablespoon of oil in saucepan set over medium heat. Add shallots; cook, stirring, for three minutes. Add potatoes to saucepan. Squeeze softened garlic heads out of skins into pot, mashing into potatoes. Pour in stock. Bring to boil. Reduce heat and simmer, uncovered, for five minutes

In batches, puree soup in food processor or blender.