Preheat oven to 400°.
Remove white papery skin from garlic heads (do not peel or separate the cloves). Wrap each head separately in foil. Bake at 400° for 45 minutes; cool 10 minutes. Separate cloves; squeeze to extract garlic pulp. Discard skins.
Cut off stems of artichokes, and remove bottom leaves. Trim about 1/2 inch from tops of artichokes. Place artichokes, stem ends down, in a large Dutch oven filled two-thirds with water; bring to a boil. Cover, reduce heat, and simmer 45 minutes or until a leaf near the center of each artichoke pulls out easily. Remove artichokes from pan.
Combine half of garlic pulp and wine in a small saucepan; bring to a boil. Cook 2 minutes. Add broth; cook until reduced to 1/2 cup (about 8 minutes). Remove from heat; stir in butter and salt. Pour mixture into a blender; add remaining half of garlic pulp. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Sprinkle dip with parsley, if desired. Serve dip with warm artichokes.