Remove white papery skin from garlic head (do not peel or separate the cloves). Wrap head in foil. Bake at 400° for 30 minutes. Remove from oven; cool.
Place potatoes in a medium saucepan, and cover with water; bring to a boil. Cook 19 minutes or until very tender. Drain, reserving 1/2 cup cooking liquid. Place potatoes in a large bowl.
Separate garlic cloves; squeeze to extract garlic pulp. Discard skins. Add pulp, yogurt, and next 6 ingredients (through red pepper) to potatoes. Mash potato mixture with a potato masher. Stir in reserved cooking liquid, 2 tablespoons at a time, until mixture is almost smooth. Sprinkle with parsley.