Preheat oven to 350°.
Remove white papery skin from garlic head (do not peel or separate cloves). Wrap garlic head in foil. Bake at 350° for 1 hour; cool 10 minutes. Separate garlic cloves; squeeze to extract garlic pulp. Discard skins.
Place potato, turnip, celeriac, and onion in a large Dutch oven; cover with water. Bring to a boil, reduce heat, and simmer 15 minutes or until vegetables are tender. Drain. Place half of vegetables in a food processor; process until smooth. Pour puréed vegetables into a bowl. Repeat procedure with the remaining vegetables.
Melt butter in pan over medium heat. Stir in garlic pulp, puréed vegetables, and cream; cook 5 minutes or until thoroughly heated, stirring frequently. Stir in the vinegar, salt, and pepper.