Preheat oven to 400 degrees. Spread squash, carrots, parsnips, sweet potato, and onion over two baking sheets and toss with enough olive oil to coat. Toss with chili powder, and a pinch of salt and pepper. Wrap head of garlic in foil and place on tray.
Roast in oven on two racks. After 20 minutes, move baking sheet on top rack to bottom rack, and sheet from bottom rack to top rack and continue to roast for another 15 minutes.
Carefully remove foil from garlic. Cut top off garlic head and squeeze garlic cloves to large stock pot, along with roasted vegetables. Add stock and bay leaves and bring to boil. Reduce to simmer, cover, and simmer on low heat for 20 minutes.
Remove pot from heat. Remove bay leaves and discard. If using immersion blender: Puree until consistency is smooth. If using a blender: Add soup to blender in batches and puree until smooth. Add salt and pepper to taste.Serve with chopped parsley and/or chives.