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