Heat oil in a large Dutch oven over medium heat. Add onion, ginger, salt, cumin, mustard, cinnamon, black pepper, and cayenne pepper. Saute for 2 minutes. Reduce heat to low; cover and cook 5 minutes until onion is tender. Add squash, sweet potato, parsnip, and broth. Bring to a boil; reduce heat, and simmer, partially covered, until tender (30 minutes). Puree vegetable mixture in a blender (in batches). Return to pot and heat through. Stir in milk; reduce heat and allow the soup to heat through, stirring occasionally.