Combine squash, corn kernels, pepper, onion, and broth in a Dutch oven; bring to a boil. Cover; reduce heat, and simmer 20 minutes. Cool.
Place half of squash mixture in a blender; process until smooth. Pour pureed squash mixture into a large bowl. Repeat procedure with the remaining squash mixture. Return mixture to pan. Stir in milk, salt, and white pepper. Cook over low heat until thoroughly heated, stirring occasionally.