Remove white papery skin from each garlic head (do not peel or separate cloves). Wrap each head separately in aluminum foil. Bake at 350° for 1 hour; let cool for 10 minutes. Separate cloves, and squeeze to extract 1/4 cup of garlic pulp; discard the skins.
Cook bacon in a large saucepan over medium-high heat until crisp. Add onion, carrot, and minced garlic, and sauté 5 minutes. Add potato, broth, salt, pepper, and bay leaf; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until potato is tender; remove bay leaf.
Combine garlic pulp and 2 cups potato mixture in a blender or food processor, and process until smooth. Return purée to pan; stir in milk, and cook over low heat until thoroughly heated. Remove from heat, and stir in chopped parsley.