Heat oil in a large stockpot over medium heat. Add onion and next 8 ingredients (onion through red pepper); sauté 2 minutes. Reduce heat to low; cover and cook 5 minutes or until onion is tender. Add squash, sweet potato, parsnip, and broth. Bring to a boil; reduce heat, and simmer, partially covered, 30 minutes or until tender.
Place one-third of vegetable mixture in a blender or food processor; process until smooth. Pour puréed vegetable mixture into a large bowl. Repeat procedure with remaining vegetable mixture. Return puréed mixture to pan; stir in milk. Cook over low heat 5 minutes or until thoroughly heated, stirring occasionally.